On the intrinsic effect of the particle size distribution on the permeability of particulate liquid chromatography columns. A theoretical overview.

This work investigates the self-assembly behavior of binary blends composed of isomeric AB diblock copolymers that share identical compositions but varying block geometries. A nonuniform distribution of side chains breaks the intrinsic symmetry along the polymer backbone, resulting in chain conformations deviating from random coils. When blocks possess complementary geometries, their conformations average out, resembling those of uniform analogs. By tuning of the degree of complementarity and blending ratio, the system undergoes phase transitions from hexagonally packed cylinders to Frank-Kasper A15 sphere and further to dodecagonal quasicrystal (DDQC) and σ phase. The side chains adjacent to the block junction dominate local packing frustration and chain stretching, thereby dictating the phase behavior. This work presents an efficient approach for precisely tuning conformational asymmetry, enabling access to complex spherical packing phases without changing the overall chemistry and composition.

Using pore-resolved direct numerical simulation (DNS), we investigate passive scalar transport at a unit Schmidt number in a turbulent flow over a randomly packed bed of spheres. The scalar is introduced at the domain’s free-slip top boundary and absorbed by the bed, which maintains a constant and uniform scalar value on the sphere surfaces. Eight cases are analysed, which are characterised by friction Reynolds numbers of ${\textit{Re}}_\tau \in [150, 500]$ and permeability Reynolds numbers of ${\textit{Re}}_{{\kern-1pt}K} \in [0.4, 2.8]$ , while flow depth-to-sphere-diameter ratios vary within $h/D \in \{ 3, 5, 10 \}$ and the roughness Reynolds numbers lie within $k_s^+ \in [20,200]$ . For cases with comparable ${\textit{Re}}_\tau$ , the permeable wall behaviour enhances scalar absorption, as indicated by increases in the Sherwood number and the scalar roughness function $\Delta c^+$ over ${\textit{Re}}_{{\kern-1pt}K}$ . At progressively higher ${\textit{Re}}_{{\kern-1pt}K}$ , the scalar absorption diverges increasingly from the momentum absorption, as its distribution peaks deeper below the crests of the sphere pack and spreads over a wider vertical region. The fixed-value scalar boundary condition emphasises certain similarities between the scalar and velocity fields. Near-interface scalar fluctuations are correlated with streamwise velocity fluctuations, and the turbulent Schmidt number remains close to its value in the free-flow region. Compared with zero-flux scalar boundary conditions, prescribing a uniform scalar value on the sphere surfaces reduces spatial heterogeneity within the pore space, thereby limiting both dispersive transport and the form-induced production of temporal scalar fluctuations.

Artificial Intelligence and Intelligent Interventional Radiology: Fusion of Human and Machine.

Abstract A major research area in discrete geometry is to consider the best way to partition the d -dimensional Euclidean space $$\mathbb {R}^d$$ R d under various quality criteria. In this paper we introduce a new type of space partitioning that is motivated by the problem of rounding noisy measurements from the continuous space $$\mathbb {R}^d$$ R d to a discrete subset of representative values. Specifically, we study partitions of $$\mathbb {R}^d$$ R d into bounded-size tiles colored by one of k colors, such that tiles of the same color have a distance of at least t from each other. Such tilings allow for error-resilient rounding, as two points of the same color and distance less than t from each other are guaranteed to belong to the same tile, and thus, to be rounded to the same point. The main problem we study in this paper is characterizing the achievable tradeoffs between the number of colors k and the distance t , for various dimensions d . On the qualitative side, we show that in $$\mathbb {R}^d$$ R d , using $$k=d+1$$ k = d + 1 colors is both sufficient and necessary to achieve $$t>0$$ t > 0 . On the quantitative side, we achieve numerous upper and lower bounds on t as a function of k . In particular, for $$d=3,4,8,24$$ d = 3 , 4 , 8 , 24 , we obtain sharp asymptotic bounds on t , as $$k \rightarrow \infty $$ k → ∞ . We obtain our results with a variety of techniques including isoperimetric inequalities, the Brunn-Minkowski theorem, sphere packing bounds, Bapat’s connector-free lemma, and Čech cohomology.

We present an analytical framework that predicts and controls nanoparticle size through external magnetic fields, uniting first-principles thermodynamics with a sphere packing approach. Calibrated to diamagnetic silver nanoparticles (20 nm at zero field and 5 nm at 250 mT), the model yields a closed-form relation between radius and field that reproduces the observed shift in most-probable size. Within the limits of classical capillarity and spherical demagnetization, the field lowers the nucleation barrier and drives the distribution toward smaller particles. Our results are robust for radii above approx 3 nm (approx 5740 atoms). Below this scale non-extensive effects likely dominate, as discussed in detail in Supplementary Information. The approach generalizes to both diamagnetic and paramagnetic systems and the limitations expected for very small or ferromagnetically ordered nanoparticles are discussed.

Abstract Here, we introduce a calibration‐less bonded‐sphere model to describe three‐dimensional, linear elastic, highly deformable particles. Voronoi tessellation is used to partition a particle into multiple sub‐spheres, generating a virtual bond network that mimics the mechanical properties of the original particle. Inter‐particle collisions are resolved by considering contacts between the contacting sub‐spheres. The model is validated through six test cases: (i) bending of a beam, (ii) stretching of a rod, (iii) contact of a deformable sphere with a flat wall, (iv) collision between two deformable spheres, (v) motion of a deformable sphere along an inclined plane, and (vi) packing of deformable spheres. The results confirm that the desired mechanical properties of the deformable particle (i.e., Young's modulus and coefficient of friction) are obtained when assigning the desired values to the virtual bonds and the sub‐spheres comprising the bond network, thereby omitting a tedious calibration process typically required by conventional bonded‐sphere models.

The Spatially Fractionated Radiotherapy (SFRT) treatment technique is characterized by its highly heterogeneous dose distribution, with an alternating pattern of high- and low-dose areas inside large tumors. For lattice SFRT, a technique that utilizes high-dose spheres, a common obstacle is maximizing the number of high-dose spheres within the tumor while maintaining spacing rules to preserve the low-dose regions. We propose a novel algorithm that uses the Rödl nibble methodology to optimize the number of lattice vertices placement for SFRT planning. By increasing the number of vertices, tumor dose metrics can be enhanced, potentially improving patient outcomes. Our new proposed algorithm, which utilizes the Rödl nibble technique, was benchmarked against the standard lattice deployment method, where the lattice centers are placed onto a rigid grid within the tumor. Both techniques used a 1.5cm diameter lattice sphere, with center-to-center spacing of 3√2cm. Twenty patients previously treated with MLC-based 3D-conformal SFRT were included in this cohort. All replans utilized four full VMAT arcs, with collimator angles in increments of 15°, 6 MV-FFF beams, and were to be delivered on a C-arm LINAC. Both sets of replans used the same optimization objectives and priorities and were prescribed a nominal dose of 15Gy to the GTV. Several benchmarking metrics were evaluated, including GTV Dmean, D10%, D50%, D90%, V50%, peak-to-valley ratio (PVDR=D10% ÷ D90%), D2cm, as well as the Dmax of nearby critical organs were evaluated. The Rödl nibble algorithm substantially increased the number of spheres (Δ mean=9.2 vertices), with an algorithm execution time of 71.26±74.43s (12.89-246.30s). This resulted in a statistically significant increase in Dmean (Δ mean=2.61Gy), D5% (Δ mean=2.22Gy), D10% (Δ mean=2.19Gy), D50% (Δ mean=2.68Gy), D90% (Δ mean=3.52Gy), and V50% (Δ mean=27.0%); however, this led to decreased PVDR (Δ mean=-6.41) and an increase in D2cm (Δ mean=1.11Gy). An increased Dmax to nearby critical organs was also observed. Overall, all Rödl nibble replans were clinically acceptable for SFRT treatments. An end-to-end example clinical case is provided to demonstrate the utility of this method. Our novel nibble algorithm significantly increased the number of lattice spheres packed within the tumor volume, resulting in enhanced dose metrics while being computationally efficient. The enhanced tumor dose metrics come with the cost of increased dose outside the tumor. As we implement this method in our clinic, further research will be directed toward site-specific optimal beam geometry to minimize dose spillage and increase the dose heterogeneity.

Characterizing the degeneracy of local stress states is a central challenge in obtaining the complete statistical mechanics of disordered media. Here, we introduce a minimal force-balance model for isolated granular clusters to probe the structure of the stress space through principal stress orientation and stress anisotropy. We further show that when complemented by physically motivated pairwise constraints, the model produces predictions for the stress alignment in packings of repulsive hard spheres. We compare these predictions against simulation data for grains in hopper and simple shear flows, finding qualitative agreement. This demonstrates the promise of modeling bulk athermal disordered systems through the combinatorics of few primitive geometric motifs.

We show that, for a standard continuously polydisperse model with particle-diameter distribution P(σ)∝σ^{-3} and polydispersity index Δ, employing a combination of standard SWAP moves and transient degree of freedom (TDOF) moves during a Lubachevsky-Stillinger-like particle-growth process dramatically increases the generated packings' jamming densities ϕ_{J}(Δ) and coordination numbers Z_{J}(Δ), for a wide range of Δ. The fractional increase in ϕ_{J}(Δ) obtained by employing these moves first increases rapidly with Δ, then plateaus at 6-7% over the range 0.1≲Δ≤0.5; the obtained ϕ_{J} are as high as 0.747 (for Δ=0.50). These density increases are achieved without producing clearly noticeable crystallization or increased fractionation, despite the fact that the packings are quite hyperstatic for all Δ>0. SWAP and TDOF moves also reduce packings' rattler populations by as much as 99% and increase their bulk moduli by as much as 80%.

Three-Dimensional Analysis of Structural Defects in Block Copolymer-Assembled Body-Centered Cubic Spherical Packing

Abstract Packing of soft spheres, such as micelles, polymer‐grafted particles, and microgels, enables the creation of diverse functional materials. Despite the importance of achieving precise structural control, understanding the kinetics of non‐equilibrium packing in a large‐scale deposition process remains challenging. This study investigates the kinetics of the precursor‐assisted close packing of soft spheres using block copolymer micelles as the sphere model. Adding the inorganic precursor SnCl4 is crucial for achieving the close packing, which is versatile and provides a robust platform for tailoring mesoporous materials with tunable pore sizes. The kinetics of the close‐packing process are explored by in situ grazing‐incidence small‐angle X‐ray scattering measurements during slot‐die coating. The soft crystallization process shows six distinct stages: dilute dispersion, concentrated dispersion, wet film, structuring wet film, gel film, and glassy film. The close packing develops first in the in‐plane direction with rapid domain growth and then advances in the out‐of‐plane direction. Precursors in the interstitial voids play a key role by mitigating packing frustration and favoring face‐centered cubic (FCC) ordering. The structure finally stabilizes into a well‐ordered FCC structure with large domain sizes. The derived mesoporous SnO2 features semiconducting properties and enhanced pore connectivity, thus showing superior gas sensing performance toward ethanol.

Abstract The effect of pore size distribution on the flow kinematics and transport properties within a three‐dimensional porous medium is investigated through numerical simulations using the Smoothed Particle Hydrodynamics (SPH) method. The method is first validated for a model porous medium within a monodisperse random spherical packing, for which the velocity distribution of the fluid flowing through the pores (i.e., the interstitial fluid velocity) and the dispersion process are found to be in both qualitative and quantitative agreement with previous experimental results. When varying the pore size distribution of the porous medium by using polydisperse beads (of different diameters), the interstitial fluid velocity distributions get narrower, and the streamlines' tortuosity decreases. This is interpreted as a result of the narrower pore size distribution reported for polydisperse microstructures. Although the dispersion process remains qualitatively the same among the investigated microstructures, with an initial ballistic trend followed by a transient seemingly anomalous regime and eventually a Fickian regime, the transverse dispersion process is found to be quantitatively reduced for polydisperse microstructure (i.e., with a narrower pore size distribution), consistently with the reported decrease in streamlines' tortuosity.

Thecrystal structures of intermetallic phases encompass a fundamentalmystery about the chemistry of metals: what drives atoms that prefersimple sphere packings as pure elements to adopt complex structures,sometimes with unit cells containing thousands of atoms? We recentlydeveloped the interface nucleus concept to interpret their most complicatedarrangements in terms of chemical pressure (CP)-driven assembliesof modules of simple parent structures. The predictions of this approachearlier led us to the Pr–Mg–Zn system and the discoveryof the modular structure of PrMg4Zn10 builtfrom MgZn2- and EuMg5-type units. Herein, wepresent the structure of a second intergrowth compound in this systemthat exhibits far greater complexity: PrMg1.6Zn5.4, whose 34.50 Å cubic unit cell contains 2,240 atoms. Its structurecan be simply decoded in terms of a 5 × 5 × 5 supercellof the Heusler structure (or alternatively a 10 × 10 × 10supercell of the body-centered cubic (BCC), structure) embedded withLaves phase fragments. The nearly seamless transition between theHeusler and Laves domains observed here reflects a simple relationshipbetween these structures, in which they can be interconverted by theexchange of a tetrahedron of atoms for a single larger atom (MgCu2 type to BCC), or vice versa (BCC to MgCu2 type).Driving forces underlying PrMg1.6Zn5.4’sstructure are inferred from the CP analysis of the parent structures,which highlight the overcompression of the Pr atoms in a model Heuslerphase and the opportunities for relief by expanded environments availableat the boundaries between the Laves and Heusler domains in PrMg1.6Zn5.4.

Sintering behavior, microstructure and dielectric properties of a novel low loss SrEr2O4 microwave ceramic

Alkali fluorides are often thought of as archetypical ionic compounds whose structures can be understood in terms of the packing of rigid spheres. At ambient pressure, they assume the rocksalt (B1) structure, while under only a few GPa of pressure, the cesium chloride (B2) structure, with higher coordination numbers, is assumed for KF, RbF, and CsF. NaF requires almost 10 times more pressure to undergo this same phase transition, which has not been observed for LiF. Herein, we provide a detailed analysis, based upon quantum chemical calculations, explaining this behavior. We show that for the heavier alkali metals, the semicore p orbitals engage in metal-metal bonding in the B2 phase, facilitating the pressure-induced B1 → B2 structural transition. These findings suggest that the semicore orbitals of heavy alkali metals can be activated without the need of strong oxidants at very mild levels of compression, resulting in the formation of chemical bonds, challenging both traditional and modern core-valence distinctions. In addition, we argue that Cs 5p-5p bonding in CsCl occurs already at ambient pressure, stabilizing the B2 phase, and suggest experiments that may be able to detect signatures of such bonding.

Developing functionalized cycloparaphenylenes (CPPs) that respond to various stimuli, particularly redox, remains challenging yet crucial for advanced nanocarbon applications. Here, we report the exploration of the synergy between the concave π-extended tetrathiafulvalene (exTTF) and the curved CPP scaffold for constructing the rigid, conjugated nanohoop exTTF[10]CPP. X-ray analysis reveals a unique spherical packing arrangement in which six adjacent nanohoops interlock through concave and convex interactions. Interestingly, fluorescence studies revealed that exTTF[10]CPP exhibited unexpected anti-Kasha emissions originating from higher excited states, along with Kasha emission from S1 excited state in toluene and THF. However, in a PMMA film, it displayed a redshifted Kasha emission. The unique Kasha/anti-Kasha dual-emission behavior represents a rarely explored photophysical phenomenon within exTTF derivatives and nanocarbon-based systems. Ultraviolet-Visible (UV-vis) absorption investigations showed that exTTF[10]CPP demonstrated reversible redox responsiveness with tunable binding affinity for C60 up to 1.92×106M-1. Notably, femtosecond transient absorption measurements further revealed a prolonged lifetime of the charge-separated state, C60 •-/exTTF[10]CPP•+, which provides sufficient time for charge utilization. This exceptional charge-transfer property enhances the photocurrent in C60⊂exTTF[10]CPP-based cast film, which is 2.43 times higher than that of exTTF[10]CPP alone, highlighting its potential in photoelectronic device.

Abstract Developing functionalized cycloparaphenylenes (CPPs) that respond to various stimuli, particularly redox, remains challenging yet crucial for advanced nanocarbon applications. Here, we report the exploration of the synergy between the concave π‐extended tetrathiafulvalene (exTTF) and the curved CPP scaffold for constructing the rigid, conjugated nanohoop exTTF[10]CPP. X‐ray analysis reveals a unique spherical packing arrangement in which six adjacent nanohoops interlock through concave and convex interactions. Interestingly, fluorescence studies revealed that exTTF[10]CPP exhibited unexpected anti‐Kasha emissions originating from higher excited states, along with Kasha emission from S1 excited state in toluene and THF. However, in a PMMA film, it displayed a redshifted Kasha emission. The unique Kasha/anti‐Kasha dual‐emission behavior represents a rarely explored photophysical phenomenon within exTTF derivatives and nanocarbon‐based systems. Ultraviolet‐Visible (UV–vis) absorption investigations showed that exTTF[10]CPP demonstrated reversible redox responsiveness with tunable binding affinity for C60 up to 1.92 × 106 M−1. Notably, femtosecond transient absorption measurements further revealed a prolonged lifetime of the charge‐separated state, C60•−/exTTF[10]CPP•+, which provides sufficient time for charge utilization. This exceptional charge‐transfer property enhances the photocurrent in C60⊂exTTF[10]CPP‐based cast film, which is 2.43 times higher than that of exTTF[10]CPP alone, highlighting its potential in photoelectronic device.

A comprehensive understanding of the unique self-assembly potential of cyclic block copolymers has long been obscured by inherent molecular uncertainties, such as linear impurities and chain-length dispersity. This study addresses these challenges through meticulous design of discrete cyclic block copolymers and their precisely matched linear counterparts. Unconventional complex spherical packings, including Frank-Kasper A15 phase, σ phase, and a quasicrystalline phase, are captured, significantly broadening the structural diversity accessible in cyclic block copolymers. Direct comparisons among the topological isomers reveal substantially deflected phase boundaries and unexpected domain size expansion in cyclic block copolymers compared to their triblock counterparts, a trend that contradicts long-standing consensus. The discrepancies arise from a competition between two opposing factors: the enhanced conformational flexibility due to the elimination of chain ends and the steric hindrance imposed by the cyclic topology. When steric effects dominate, the increased conformational asymmetry in cyclic block copolymers stabilizes unconventional spherical phases and enlarges overall domain sizes. The precisely engineered macromolecules eliminate disruptive effects from confounding chemical defects, offering an ideal platform for systematic and quantitative investigation into how chain architecture governs self-assembly and molecular packing.

Abstract Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle rearrangements are represented by interacting spin flips called hysterons, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects and how such objects interact with one another. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings and select pairs of rearrangements that undo one another to create periodic cyclic behavior. We find that the rearrangement pairs surprisingly persist down to the smallest increments in strain, even in the smallest systems we can study. We explore the statistics of these rearrangement pairs and find that there is a relation between the amount of hysteresis and the energy drop and mean-square displacement of the particles; these results are inconsistent with the scaling found in models that treat rearrangements as localized buckling events. Finally, our analysis shows that there is no clean distinction between the particle motions that represent the identity of a single, individual rearrangement and the particle motions that lead to interactions between separated rearrangements or hysterons. These results offer insight into how complex systems such as amorphous solids can reach a limit cycle.