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Results for “Sphere packings”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Geometric and topological entropies of sphere packing

Here, we present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D. The theory generalizes concepts of granular and glassy configurational entropies for the case of nonjammed systems. It is directly applicable to sticky colloids and predicts an asymptotic phase behavior of sticky spheres in the limit of strong binding.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Impact of peripheral alkyl chain length on mesocrystal assemblies of G2 dendrons

Unique sphere-packing mesophases such as Frank–Kasper (FK) phases have emerged from the viable design of intermolecular interactions in supramolecular assemblies. In this work, a series of C n -G2-CONH 2 dendrons possessing an identical core wedge are investigated to elucidate the impact of peripheral alkyl chain lengths (C n ) on the formation of the close-packed structures. The C 18 and C 14 dendrons, of which the contour lengths of the periphery L p are longer than the wedge length L w , assemble into a uniform sphere-packing phase such as body-centred cubic (BCC), whereas the C 8 dendron with short (L p < L w ) corona environment forms the FK A15 phase. Particularly in the intermediate C 12 and C 10 dendrons (L p ≈ L w ), cooling the samples from an isotropic state leads to cooling-rate-dependent phase behaviours. The C 12 dendron produces two structures of hexagonal columnar and sphere-packing phases (BCC and A15), while the C 10 dendron generates the A15 and σ phases by the fast- and slow-cooling processes, respectively. Our results show the impact of peripheral alkyl chain lengths on the formation of mesocrystal phases, where the energy landscape of the dendrons at L p /L w ≈ 1 must be more complex and delicate than those with either longer or shorter peripheral alkyl chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Modifying Frank–Kasper Mesophases by Modulating Chain Configuration in PDMS- b -PTFEA Copolymers

The common spherical mesophases observed from chemically distinct compounds have promoted extensive studies of packing structures in soft-matter self-assemblies. In this report we present a new approach for controlling sphere-packing phases by modulating homologous copolymer chain configurations. To this end, three sets of sample pairs, compositionally asymmetric polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) diblock copolymers (diBCPs) and their homologues containing the corresponding triblock copolymer (triBCP), are synthesized via atom transfer radical polymerization and designed with the consistent volume fractions of the core-forming PTFEA block, f PTFEA = 0.20, 0.18, and 0.15. We identify the formation of C15 and hexagonally close-packed (HCP) phases in the triBCP-containing PDMS-b-PTFEAs, whereas the sigma and C14 phases are formed in their diBCP analogues, respectively. These phase shifts into C15 and HCP, due to molecular configuration differences, reveal a significant yet unrealized role of chain configurations and the associated chain size effects in determining the stable sphere-packing phases in BCP systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Various Low-Symmetry Phases in High- χ and Conformationally Asymmetric PDMS- b -PTFEA Copolymers

Since the discovery of the Frank–Kasper (FK) phase a decade ago, single-component block copolymer systems have offered unique opportunities to explore the structural and phase-transition properties of topologically close-packed FK phases composed of point-particle motifs. Here, we present the formation of complex low-symmetry phases and their thermodynamic stability using high-χ and high-ε linear diblock copolymers, where χ and ε are the Flory–Huggins interaction parameter and conformational asymmetry between the two blocks, respectively. In this work, a series of polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) copolymers are prepared by tuning the volume fraction ($f_{\text{PTFEA}}$) of a minor PTFEA block. The packing structures of PDMS-b-PTFEAs are mapped in the space of temperature versus $f_{\text{PTFEA}}$ using X-ray scattering measurements. In addition to the packing structures reported earlier, we identify another A15 phase at higher $f_{\text{PTFEA}}$ close to a hexagonally packed cylinder (HEX) phase and establish the phase sequence of HEX–A15–σ–C14–BCC with decreasing $f_{\text{PTFEA}}$. Theoretical calculation of relative free-energy densities confirms the experimental phase sequence of the composition-dependent sphere-packing structures. Interestingly, the domain sizes of three-dimensional (3D) sphere-packing structures are nearly temperature-invariant compared to that of a two-dimensional HEX structure, and we attribute this dimensional stability to the strong enthalpic effects in the formation of 3D packing structures and the geometrical characteristics of spherical domains. Our results demonstrate that the interaction parameter χ, together with the known role of conformational asymmetry ε, serves as the primary thermodynamic parameter for selecting and stabilizing various low-symmetry packing structures in sphere-forming linear diblock copolymer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Random Close Packing as a Dynamical Phase Transition

Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction Φ FCC = π / √ 18 ≈ 0.74 . The densest “random packing,” random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value Φ RCP ≈ 0.64 . We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point Φ cmax ≈ 0.64 ≈ Φ RCP and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Apex hydrogen bonds in dendron assemblies modulate close-packed mesocrystal structures

The close-packed mesocrystal structures from soft-matter assemblies have recently received attention due to their structural similarity to atomic crystals, displaying various sphere-packing Frank–Kasper (FK) and quasicrystal structures. Herein, diverse mesocrystal structures are explored in second-generation dendrons (G2-X) designed with identical wedges, in which the terminal functionalities X = CONH 2 and CH 2 NH 2 represent two levels of the strong and weak hydrogen-bonding apexes, respectively. The cohesive interactions at the core apex, referred to as the core interactions, are effectively modulated by forming heterogeneous hydrogen bonds between these two functional units. For the dendron assemblies compositionally close to each pure component of G2-CONH 2 and G2-CH 2 NH 2 , their own FK A15 and C14 phases dominate other phases, respectively. We show the existence of the wide-range FK σ including the dodecagonal quasicrystal (DDQC) phases from the dendron mixtures between G2-CONH 2 and G2-CH 2 NH 2 , providing an experimental phase sequence of A15–σ–DDQC–C14 as the core interactions are alleviated. Intriguingly, the temperature dependence of particle sizes shows that the high plateau values of particle sizes are maintained equivalently until each threshold temperature (T th ), followed by a prompt decrease above the T th . A decrease in T th by alleviating the core interactions and its composition dependence suggest that the more size-dispersed particles, the more susceptibility to chain exchange with increasing temperature. Here our results on the formation of supramolecular dendron assemblies provide a guide to understand the core-interaction-dependent mesocrystal structures toward the fundamental principle underlying the temperature dependence of their particle sizes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network

The study of solute transport in porous media is of interest in many chemical engineering systems. Some example applications include packed bed catalytic reactors, filtration devices, and batteries. The pore scale modeling of these systems is time consuming and may require large computing resources, for this reason computational fluid dynamics (CFD) simulations are not practical if a large number of simulations is required, like in multiscale modeling, where a model at a large scale calls for pore scale simulations. It has been shown that neural networks can be trained with a dataset of flow simulations and then predict fields orders of magnitude faster, and with less computational resources, in new domains. However, it is crucial to provide the neural network with an effective description of the domain and the undergoing operating conditions to be able to train models that generalize accurately in unseen samples. Therefore, research is needed to employ neural networks in new complex systems. The appropriate training of a network for predicting coupled flow and solute transport processes is an outstanding problem due to the complex interplay between geometry and operating conditions. In this work, we train a multi scale convolutional neural network (MSNet) with a diverse dataset of simulations of transport and chemical reaction in porous media to predict the local concentration fields in images of porous media. Our dataset contains a wide diversity of sphere pack arrangements under different operating conditions (Péclet and Reynolds numbers). Further, we train a robust model by employing different input descriptors that represent the medium and the different operating conditions of each system. Our trained model is able to provide nearly instantaneous predictions, compared to around twenty hours of the CFD workflow, with less than 3.5% error on new geometries and transport conditions. Thus the model could be easily integrated in a multiscale workflow where fast response is needed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Efficient reconstruction and validation of heterogeneous microstructures for energy applications

The digital reconstruction of microstructures is necessary for simulations in fields ranging from geology to electrochemistry, but the state-of-the-art digital reconstruction techniques often compromise between resolution and field of view. It is challenging to retain detailed microstructure information in large-scale reconstructions. Here, this study investigates different aspects of the Yeong-Torquato algorithm based on correlation functions to make it more efficient. We achieve this goal by reducing the computational complexity of the chord-length distribution function and the two-point correlation function, applying the random sphere-packing method as the initial condition, and restricting potential voxel swaps to interfaces. In addition, a novel superposition parallel scheme is introduced to aid in searching for potential voxel swaps. The algorithm proposed is validated by comparing the pore-size distributions of reconstructed 3D custom battery electrodes from a sample dataset obtained from transmission X-ray microscopy. From a sample image with 200 x 200 pixels, the code can reconstruct a 300 x 300 x 300 structure in under 22 h and reconstruct a 400 x 400 x 400 structure in 43 h with eight cores.

42 ENGINEERING↗
DOE OSTI2023

Bootstrapping boundaries and branes

The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

We report three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

02 PETROLEUM↗
DOE OSTI2022

Probing the solidification of quasicrystals via joint experiment and simulation (Final Report)

Quasicrystals (QCs) possess long-range positional order but non-crystallographic orientational order. Their classically ‘forbidden’ symmetry has long attracted the interest of scientists worldwide. Despite their frequent observation in both metal alloys and soft matter structures in the 35 years since their discovery, little is known about how QCs evolve from a liquid, amorphous, or crystalline precursor. In this project, we sought to resolve the enigma of QC self-assembly through a combined experimental and computational program. The Shahani group employed in situ electron and synchrotron X ray imaging to peer into the growth dynamics of QCs in a liquid, covering a broad range of length scales and solidification pathways. Glotzer's team developed new simulation models incorporating phasonic defects — which are unique to quasicrystals — and used this model to investigate two grains growing together, closely mimicking the experimental conditions. While QCs remain exceptional structures, most compounds in the realm of intermetallics adopt non-trivial geometries. In fact, only around 6% of phases are comprised of the simplest sphere packings that researchers so readily associate with metals. State-of-the-art knowledge of phase transformations at the outset of this collaborative project did not encompass the remaining 94% of intermetallic compounds that possess complex and aperiodic structure types. Therefore, we expect that outcomes from this project will have immediate and profound impact on synthesis and processing science: our efforts will be used to not only explain the growth dynamics of QCs but also complex intermetallics more broadly.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Granular packings with sliding, rolling, and twisting friction

Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The influence of packing structure and interparticle forces on ultrasound transmission in granular media

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

36 MATERIALS SCIENCE↗