Application of polyhedron model to predict heat capacity of mixed oxides
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Arias-Hernandez, Jesus Alejandro (ORCID:0009000333↗
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Multi-plane moment-of-fluid interface reconstruction in 3D
Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.
3D interface reconstruction↗
Sharp front tracking with geometric interface reconstruction
Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.
42 ENGINEERING↗
Organic Modulators Enable Morphological Diversity in Colloidal Crystals Engineered with DNA
Colloidal crystal engineering with DNA is a powerful way of generating a wide variety of crystals spanning over 90 different symmetries. However, in many cases, crystals with well-defined habits are difficult, if not impossible, to make, in part due to rapid crystal defect formation and propagation. This is especially true in the case of face-centered cubic (FCC) structures. Herein, we report a strategy that uses formamide as a chemical modulator to slow down colloidal crystal growth, which decreases defect formation and yields higher-quality crystals. Formamide forms hydrogen bonds with DNA bases and destabilizes the DNA duplex; in the context of colloidal crystallization, formamide leads to the disassembly of undercoordinated particles (defect architectures) and facilitates their reassembly into structures with the maximum number of nearest-neighbor contacts and DNA bonds. Here, when targeting an FCC lattice comprised of DNA-modified spherical 20 nm particles, formamide promotes the formation of its Wulff polyhedron (a truncated octahedron), never observed before in colloidal crystal engineering with DNA. Importantly, kinetic habits, including tetrahedra, octahedra, icosahedra, and decahedra, are also observed depending on formamide concentration.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Towards libraries of different ultrasmall amorphous silica cage topologies
Cage topology controlled at the nanometer length scale is expected to enable original functionalities, e.g., in catalysis and therapeutics. Cages are fundamental structural motifs of clathrates and their topological duals, Frank-Kasper phases, and are constituents of mesoporous silica frameworks. However, with one exception, they have not been synthesized as discrete particles. By varying reactant ratios of surfactant, oil, and silane, we report the discovery of 5(12)6(2) and 5(12)6(8) amorphous silica polyhedra, each coexisting with the previously identified 5(12) cage, using combined cryo-transmission electron microscopy (cryo-TEM) and single-particle reconstruction (SPR). Notably, the 5(12)6(8) polyhedron represents a topology not previously observed in mesoporous silica frameworks. Control over structural features is demonstrated, and insights into cage formation mechanisms are provided. Structural outcomes are summarized in a ternary morphology diagram alongside prior results, bridging serendipitous discovery and intentional design of silica cages displaying a level of control over silica polymerization rivaling nature.
Jang, Dong June [Department of Materials Science a↗