Quantifying Shape of Star-Like Objects Using Shape Curves and A New Compactness Measure

Shape is an important indicator of the physical and chemical behavior of natural and engineered particulate materials (e.g., sediment, sand, rock, volcanic ash). It directly or indirectly affects numerous microscopic and macroscopic geologic, environmental and engineering processes. Due to the complex, highly irregular shapes found in particulate materials, there is a perennial need for quantitative shape descriptions. We developed a new characterization method (shape curve analysis) and a new quantitative measure (compactness, not the topological mathematical definition) by applying a fundamental principle that the geometric anisotropy of an object is a unique signature of its internal spatial distribution of matter. We show that this method is applicable to “star-like” particles, a broad mathematical definition of shape fulfilled by most natural and engineered particulate materials. This new method and measure are designed to be mathematically intermediate between simple parameters like sphericity and full 3D shape descriptions. For a “star-like” object discretized as a polyhedron made of surface planar elements, each shape curve describes the distribution of elemental surface area or volume. Using several thousand regular and highly irregular 3-D shape representations, built from model or real particles, we demonstrate that shape curves accurately encode geometric anisotropy by mapping surface area and volume information onto a pair of dimensionless 2-D curves. Each shape curve produces an intrinsic property (length of shape curve) that is used to describe a new definition of compactness, a property shown to be independent of translation, rotation, and scale. Compactness exhibits unique values for distinct shapes and is insensitive to changes in measurement resolution and noise. With increasing ability to rapidly capture digital representations of highly irregular 3-D shapes, this work provides a new quantitative shape measure for direct comparison of shape across classes of particulate materials

Electrosteric Control Of The Aggregation And Yielding Behavior Of Concentrated Portlandite Suspensions

Portlandite (calcium hydroxide: CH: Ca (OH)2) suspensions aggregate spontaneously and form percolated fractal aggregate networks when dispersed in water. Consequently, the viscosity and yield stress of portlandite suspensions diverge at low particle loadings, adversely affecting their processability. Even though polycarboxylate ether (PCE)-based comb polyelectrolytes are routinely used to alter the particle dispersion state, water demand, and rheology of similar suspensions (e.g., ordinary portland cement suspensions) that feature a high pH and high ionic strength, their use to control portlandite suspension rheology has not been elucidated. This study combines adsorption isotherms and rheological measurements to elucidate the role of PCE composition (i.e., charge density, side chain length, and grafting density) in controlling the extent of PCE adsorption, particle flocculation, suspension yield stress, and thermal response of portlandite suspensions. We show that longer sidechain PCEs are more effective in affecting suspension viscosity and yield stress, in spite of their lower adsorption saturation limit and fractional adsorption. The superior steric hindrance induced by the longer side chain PCEs results in better efficacy in mitigating particle aggregation even at low dosages. However, when dosed at optimal dosages (i.e., a dosage that induces a dynamically equilibrated dispersion state of particle aggregates), different PCE-dosed portlandite suspensions exhibit identical fractal structuring and rheological behavior regardless of the side chain length. Furthermore, it is shown that the unusual evolution of the rheological response of portlandite suspensions with temperature can be tailored by adjusting the PCE dosage. The ability of PCEs to modulate the rheology of aggregating charged particle suspensions can be generally extended to any colloidal suspension with a strong screening of repulsive electrostatic interactions

Ultrafast Stiffening of Concentrated Thermoresponsive Mineral Suspensions

Extrusion-based 3D printing with rapidly hardening polymeric materials is capable of building almost any conceivable structure. However, concrete, one of the most widely used materials for large-scale structural components, is generally based on inorganic binder materials like Portland cement. Unlike polymeric materials, a lack of precise control of the extent and rate of solidification of cement-based suspensions is a major issue that affects the ability to 3D-print geometrically complex structures. Here, we demonstrate a novel method for controllable-rapid solidification of concentrated mineral suspensions that contain a polymer binder system based on epoxy and thiol precursors as well as one or more mineral fillers like quartz and calcite. The thermally triggered epoxy-thiol condensation polymerization induces rapid stiffening of the hybrid suspensions (0.30 ≤ ϕ ≤ 0.60), at trigger temperatures ranging between 50 °C and 90 °C achieving average stiffening rates up to 400 Pa/s. The use of nucleophilic initiators such as 1-methylimidazole provides control over the activation temperature and curing rate, thereby helping to achieve an adjustable induction period and excellent thermal latency. By using multiple techniques, we provide guidelines to create designer compositions of mineral suspensions that utilize thermal triggers to achieve thermal latency and ultrafast stiffening – prerequisite attributes for 3D-manufacturing of topologically-optimized structural components

Structural Evidence of T Cell Xeno-reactivity in the Absence of Molecular Mimicry

The T cell receptor (TCR), from a xeno-reactive murine cytotoxic T lymphocyte clone AHIII12.2, recognizes murine H-2Db complexed with peptide p1027 (FAPGVFPYM), as well as human HLA-A2.1 complexed with peptide p1049 (ALWGFFPVL). A commonly proposed model (the molecular mimicry model) used to explain TCR cross-reactivity suggests that the molecular surfaces of the recognized complexes are similar in shape, charge, or both, in spite of the primary sequence differences. To examine the mechanism of xeno-reactivity of AHIII12.2, we have determined the crystal structures of A2/p1049 and Db/p1027 to 2.5 Å and 2.8 Å resolution, respectively. The crystal structures show that the TCR footprint regions of the two class I complexes are significantly different in shape and charge. We propose that rather than simple molecular mimicry, unpredictable arrays of common and differential contacts on the two class I complexes are used for their recognition by the same TCR

Advances in shape measurement in the digital world

The importance of particle shape in terms of its effects on the behaviour of powders and other particulate systems has long been recognised, but particle shape information has been rather difficult to obtain and use until fairly recently, unlike its better-known counterpart, particle size. However, advances in computing power and 3D image acquisition and analysis techniques have resulted in major progress being made in the measurement, description and application of particle shape information in recent years. Because we are now in a digital era, it is fitting that many of these advanced techniques are based on digital technology. This review article aims to trace the development of these new techniques, highlight their contributions to both academic and practical applications, and present a perspective for future developments

Bridging the Gap Between Random Microstructure and 3D Meshing

There are different ways to mathematically represent three-dimensional (3D) heterogeneous material microstructures. It is desirable to pick the representation that best bridges the gap between heterogeneous microstructure and computer-aided engineering finite element analysis. 3D cubic meshes of brick (voxel) elements can be generated for digital structures (e.g., from X-ray CT), but this work describes how simplified tetrahedral meshes, more suitable for complex mechanical problems, including crack generation, can be implemented. The mathematical representations of heterogeneous material structures considered in this paper include (1) 3D digital image microstructure, exemplified by the Virtual Cement and Concrete Testing Laboratory (VCCTL); (2) X-ray computed tomography (CT) images stacked into a 3D digital image; and (3) real-shaped sand and gravel particles, represented by spherical harmonic series, randomly placed into a 3D box to make a virtual concrete microstructure. The approach used involves a topological structure suitable for stereo lithography file (STL) representation and the development of algorithms for topological and geometric data processing to obtain a 3D simplified tetrahedral mesh that incorporates the random material structure. Mesh simplification is obtained through a set of remeshing tools to improve element quality and reduce the number of elements. During the mesh generation procedure, we combine both the aggregates and the cement paste matrix to ensure perfectly coinciding nodes at their interface. Based on the proposed procedures, a simplified surface and volume mesh of heterogeneous systems can be generated with data consistencies (e.g., no overlapping, no gap at the interfaces)

Local elastic moduli of simple random composites computed at different length scales

Techniques like nanoindentation and atomic force microscopy can estimate the local elastic moduli in a region surrounding the probe used. For composites with phase regions much larger than the size of the probe, these procedures can identify the phases via their different elastic moduli but identifying phase regions that are on the same size scale as the indent is more problematic. This paper looks at three random 3D 8003 voxel composite models, each consisting of a matrix and spherical inclusions. One model has non-overlapping spheres and two models have overlapping spheres, with two and three distinct phases. The linear elastic problem is solved for each microstructure, and histograms are made of the local Young’s moduli over a number of sub-volumes (SVs), averaged over progressively larger SVs. The number and shape of histogram peaks change from N delta functions, where N is the number of elastically distinct phases, at the 1 voxel SV limit, to a single delta function located at the value of the effective global Young’s modulus, when the SV equals the unit cell volume. The phase volume fractions are also tracked for each bin in the Young’s modulus histograms, showing the phase make-up of bin in the histogram. There are clear differences seen between the non-overlapping and three-phase overlapping models and the two-phase overlapping sphere model, because of different size microstructural features, characterized by the average value of size as computed by the W(q) function. In the three-phase model, a peak that is originally all phase 3 persists at its same location, but as the size of the SVs increase, it is made up of a mixture of phases, so that it cannot be identified with a single phase even though it remains a clear peak. These results give some guidance as to what probe size might be useful in distinguishing different phases by local elastic moduli measurements, and how the length scales of the probe and the microstructure interact.ISSN:1359-5997ISSN:0025-5432ISSN:1871-687