Length Scales Research Articles

Video frame interpolation neural network for 3D tomography across different length scales

Three-dimensional (3D) tomography is a powerful investigative tool for many scientific domains, going from materials science, to engineering, to medicine. Many factors may limit the 3D resolution, often spatially anisotropic, compromising the precision of the information retrievable. A neural network, designed for video-frame interpolation, is employed to enhance tomographic images, achieving cubic-voxel resolution. The method is applied to distinct domains: the investigation of the morphology of printed graphene nanosheets networks, obtained via focused ion beam-scanning electron microscope (FIB-SEM), magnetic resonance imaging of the human brain, and X-ray computed tomography scans of the abdomen. The accuracy of the 3D tomographic maps can be quantified through computer-vision metrics, but most importantly with the precision on the physical quantities retrievable from the reconstructions, in the case of FIB-SEM the porosity, tortuosity, and effective diffusivity. This work showcases a versatile image-augmentation strategy for optimizing 3D tomography acquisition conditions, while preserving the information content.

Bridging Innovations of Phase Change Heat Transfer to Electrochemical Gas Evolution Reactions.

Bubbles play a ubiquitous role in electrochemical gas evolution reactions. However, a mechanistic understanding of how bubbles affect the energy efficiency of electrochemical processes remains limited to date, impeding effective approaches to further boost the performance of gas evolution systems. From a perspective of the analogy between heat and mass transfer, bubbles in electrochemical gas evolution reactions exhibit highly similar dynamic behaviors to them in the liquid-vapor phase change. Recent developments of liquid-vapor phase change systems have substantially advanced the fundamental knowledge of bubbles, leading to unprecedented enhancement of heat transfer performance. In this Review, we aim to elucidate a promising opportunity of understanding bubble dynamics in electrochemical gas evolution reactions through a lens of phase change heat transfer. We first provide a background about key parallels between electrochemical gas evolution reactions and phase change heat transfer. Then, we discuss bubble dynamics in gas evolution systems across multiple length scales, with an emphasis on exciting research problems inspired by new insights gained from liquid-vapor phase change systems. Lastly, we review advances in engineered surfaces for manipulating bubbles to enhance heat and mass transfer, providing an outlook on the design of high-performance gas evolving electrodes.

Causal fermion systems as an effective collapse theory

Abstract It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr"odinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski-Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale~$\ell_{\min}$.

The role of the water contact layer on hydration and transport at solid/liquid interfaces

Understanding the structure in the nanoscopic region of water that is in direct contact with solid surfaces, so-called contact layer, is key to quantifying macroscopic properties that are of interest to e.g. catalysis, ice nucleation, nanofluidics, gas adsorption, and sensing. We explore the structure of the water contact layer on various technologically relevant solid surfaces, namely graphene, MoS[Formula: see text], Au(111), Au(100), Pt(111), and Pt(100), which have been previously hampered by time and length scale limitations of ab initio approaches or force field inaccuracies, by means of molecular dynamics simulations based on ab initio machine learning potentials built using an active learning scheme. Our results reveal that the in-plane intermolecular correlations of the water contact layer vary greatly among different systems: Whereas the contact layer on graphene and on Au(111) is predominantly homogeneous and isotropic, it is inhomogeneous and anisotropic on MoS[Formula: see text], on Au(100), and on the Pt surfaces, where it additionally forms two distinct sublayers. We apply hydrodynamics and the theory of the hydrophobic effect, to relate the energy corrugation and the characteristic length-scales of the contact layer with wetting, slippage, the hydration of small hydrophobic solutes and diffusio-osmotic transport. Thus, this work provides a microscopic picture of the water contact layer and links it to macroscopic properties of liquid/solid interfaces that are measured experimentally and that are relevant to wetting, hydrophobic solvation, nanofluidics, and osmotic transport.

Thermal preconditioning of membrane stress to control the shapes of ultrathin crystals.

We employ the phospholipid bilayer membranes of giant unilamellar vesicles as a free-standing environment for the growth of membrane-integrated ultrathin phospholipid crystals possessing a variety of shapes with 6-fold symmetry. Crystal growth within vesicle membranes, where more elaborate shapes grow on larger vesicles is dominated by the bending energy of the membrane itself, creating a means to manipulate crystal morphology. Here we demonstrate how cooling rate preconditions the membrane tension before nucleation, in turn regulating nucleation and growth, and directing the morphology of crystals by the time they are large enough to be visualized. The crystals retain their shapes during further growth through the two phase region. Experiments demonstrate this behavior for single crystals growing within the membrane of each vesicle, ultimately comprising up to 13% of the vesicle area and length scales of up to 50 microns. A model for stress evolution, employing only physical property data, reveals how the competition between thermal membrane contraction and water diffusion from tensed vesicles produces a size- and time-dependence of the membrane tension as a result of cooling history. The tension, critical in the contribution of bending energy in the fluid membrane regions, in turn selects for crystal shape for vesicles of a given size. The model reveals unanticipated behaviors including a low steady state tension on small vesicles that allows compact domains to develop, rapid tension development on large vesicles producing flower-shaped domains, and a stress relaxation through water diffusion across the membrane with a time constant scaling as the square of the vesicle radius, consistent with measurable tensions only in the largest vesicles.

Multiple states of two-dimensional turbulence above topography

The recent work of Siegelman & Young (Proc. Natl Acad. Sci. USA, vol. 120, issue 44, 2023, e2308018120) revealed two extreme states reached by the evolution of unforced and weakly damped two-dimensional turbulence above random rough topography, separated by a critical kinetic energy $E_\#$ . The low- and high-energy solutions correspond to topographically locked and roaming vortices, surrounded by non-uniform and homogeneous background potential vorticity (PV), respectively. However, we found that these phenomena are restricted to the particular intermediate length scale where the energy was initially injected into the system. Through simulations initialized by injecting the energy at larger and smaller length scales, we found that the long-term state of topographic turbulence is also dependent on the initial length scale and thus the initial enstrophy. If the initial length scale is comparable to the domain size, the long-term flow field resembles the minimum-enstrophy state proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129–154), with very few topographically locked vortices; the long-term enstrophy is quite close to the minimum value, especially when the energy is no larger than $E_\#$ . As the initial length scale becomes smaller, more vortices nucleate and become more mobile; the long-term enstrophy increasingly deviates from the minimum value. Simultaneously, the background PV tends to homogenization, even if the energy is below $E_\#$ . These results complement the phenomenology of topographic turbulence documented by Siegelman & Young, by showing that the minimum-enstrophy and background PV homogenization states can be adequately approached by large- and small-scale initial fields, respectively, with relatively arbitrary energy.

Impact of Synthesis Method on the Structure and Function of High Entropy Oxides.

The term sample dependence describes the troublesome tendency of nominally equivalent samples to exhibit different physical properties. High entropy oxides (HEOs) are a class of materials where sample dependence has the potential to be particularly profound due to their inherent chemical complexity. In this work, we prepare a spinel HEO of identical nominal composition by five distinct methods, spanning a range of thermodynamic and kinetic conditions: solid state, high pressure, hydrothermal, molten salt, and combustion syntheses. By structurally characterizing these five samples across all length scales with a variety of X-ray methods, we find that while the average structure is unaltered, the samples vary significantly in their local structures and their microstructures. The most profound differences are observed at intermediate length scales, both in terms of crystallite morphology and cation homogeneity. As revealed by X-ray fluorescence microscopy ideal cation homogeneity is achieved only in the case of combustion synthesis. These structural differences in turn significantly alter the observed functional properties, which we demonstrate via characterization of their magnetic response. While ferrimagnetic order is retained across all five samples, the sharpness of the transition, the size of the saturated moment, and the coercivity all show marked variations with synthesis method. We conclude that the chemical flexibility inherent to HEOs is complemented by strong synthesis method dependence, providing another axis along which to optimize these materials for a wide range of applications.

Free energy and extension of stiff polymer chains confined in nanotubes with diverse cross-sectional shapes

The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.

Stratified Resistive Tearing Instability

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

Learning grain boundary segregation behavior through fingerprinting complex atomic environments

Although continuum-scale segregation is a well-documented behavior in multi-species materials, detailed site-specific behavior remains largely unexplored. This is partially due to the complexity of analyzing materials at the requisite time and length scales for describing segregation with full atomic accuracy. Here, we better evaluate the segregation behavior of disordered grain boundary (GB) atomic environments through leveraging a set of Strain Functional Descriptors (SFDs) to generate an atomic descriptor (i.e., fingerprint). Using this atomic fingerprint, we resolve key relationships between atomic structure and segregation energy. Machine learning (ML) techniques are utilized in concert with this SFD fingerprint to elucidate complex relationships relating segregation potential to changes in specific features of the local Gaussian density captured by the SFDs. Finally, we identify relationships that indicate both individual and joint structure-property correlations. Linking atomic segregation energy to key structural features demonstrates the value of higher-order descriptors for uncovering complex structure-property relationships at an atomic scale.

Physical Mechanisms of Improved Performance of Scaffolded Zinc-Silver Battery Cathodes.

Nanostructuring can greatly improve the electrode stability of rechargeable battery systems, such as Zn-Ag. In this report, we investigate the physical mechanisms by which nanostructuring alters structural properties of nanomaterials and thereby influences the structural stability of electrodes. We specifically consider the effects of Au-based nanoscaffolds on Ag. Through density functional theory calculations, we propose that the charge transfer at the Au-Ag interface can facilitate the formation of Ag2O from Ag centers. Structural analysis of samples prepared in this work shows that Ag2O is extruded from Au-Ag material in the form of sheets. Interestingly, the length scale of such protrusions depends on the Au mole fraction that significantly alters the system's overall structural morphology. We rationalize these findings via kinetic Monte Carlo simulations of the Ag2O growth process and highlight the role of Au as a heterogeneous nucleation center.

A classical density functional theory for solvation across length scales.

A central aim of multiscale modeling is to use results from the Schrödinger equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level on length scales that vastly exceed what is accessible to molecular simulations.

Quasi-two-dimensionality of three-dimensional, magnetically dominated, decaying turbulence

Decaying magnetohydrodynamic (MHD) turbulence is important in various astrophysical contexts, including early universe magnetic fields, star formation, turbulence in galaxy clusters, magnetospheres and solar corona. Previously known in the nonhelical case of magnetically dominated decaying turbulence, we show that magnetic reconnection is important also in the fully helical case and is likely the agent responsible for the inverse transfer of energy. Again, in the fully helical case, we find that there is a similarity in power law decay exponents in both 2.5D and 3D simulations. To understand this intriguing similarity, we investigate the possible quasi-two-dimensionalization of the 3D system. We perform Minkowski functional analysis and find that the characteristic length scales of a typical magnetic structure in the system are widely different, suggesting the existence of local anisotropies. Finally, we provide a quasi-two-dimensional hierarchical merger model which recovers the relevant power law scalings. In the nonhelical case, we show that a helicity-based invariant cannot constrain the system, and the best candidate is still anastrophy or vector potential squared, which is consistent with the quasi-two-dimensionalization of the system.

Advanced Characterization of the Spatial Variation of Moiré Heterostructures and Moiré Excitons.

In this short review, an overview of recent progress in deploying advanced characterization techniques is provided to understand the effects of spatial variation and inhomogeneities in moiré heterostructures over multiple length scales. Particular emphasis is placed on correlating the impact of twist angle misalignment, nano-scale disorder, and atomic relaxation on the moiré potential and its collective excitations, particularly moiré excitons. Finally, future technological applications leveraging moiré excitons arediscussed.

Cross-gradient joint inversion and clustering of ERT and SRT data on structured meshes incorporating topography

Summary The combination of electrical resistivity and seismic refraction tomography is a common practice for the characterization of subsurface features. Presently, the cross-gradient inversion scheme stands out as one of the most robust joint approaches, and some authors modified it to manage complex topographies on unstructured meshes even if at the expense of introducing additional parameters in the inversion process. We propose in this work a cross-gradient algorithm for jointly inverting electrical and seismic tomographic data on structured meshes in cases with non-flat topography. The proposed approach preserves the benefit of the classical cross-gradient approach without the need to impose physical length scales, as for irregular meshes. The quality of the results is evaluated in comparison with independent inversion through a new standardized cross-gradient index and a fuzzy c-means analysis that provides an assessment of the reconstruction accuracy through the membership function. The proposed method was applied to both synthetic models and field-scale examples located in Central Italy, where an accurate geophysical reconstruction is needed for the rehabilitation of existing dams. For all cases, joint inversion yielded superior results compared to independent inversion, demonstrating better agreement with available borehole data. The effectiveness of the joint approach was also demonstrated by the post-inversion tools, where the new cross-gradient index highlighted changes in structural similarity whilst fuzzy c-means clustering allowed for a quantitative reconstruction (position and shape) of the main units at the sites, facilitating the detection of site layering modifications.

Quantitative matching of forensic evidence fragments using fracture surface topography and statistical learning

The complex jagged trajectory of fractured surfaces of two pieces of forensic evidence is used to recognize a “match” by using comparative microscopy and tactile pattern analysis. The material intrinsic properties and microstructures, as well as the exposure history of external forces on a fragment of forensic evidence have the premise of uniqueness at a relevant microscopic length scale (about 2–3 grains for cleavage fracture), wherein the statistics of the fracture surface become non-self-affine. We utilize these unique features to quantitatively describe the microscopic aspects of fracture surfaces for forensic comparisons, employing spectral analysis of the topography mapped by three-dimensional microscopy. Multivariate statistical learning tools are used to classify articles and result in near-perfect identification of a “match” and “non-match” among candidate forensic specimens. The framework has the potential for forensic application across a broad range of fractured materials and toolmarks, of diverse texture and mechanical properties.

Strategic alloy design and processing for improved mechanical response in the Mo-Si-Ti system

This study focuses on the impact of off-eutectic microstructures on mechanical properties in ternary Mo-Si-Ti alloys, namely Ti-rich Mo-18Si-72Ti and Mo-16.5Si-72Ti, in relation to the well-researched eutectic, two-phase Mo-20Si-52.8Ti alloy. The microstructure of these alloys consists of a Ti-rich body-centered cubic solid solution (Ti,Mo,Si)ss and a hexagonal silicide phase (Ti,Mo)5Si3. Notably, the off-eutectic alloys exhibit remarkable compression ductility at 800 °C, distinguishing it from Mo-20Si-52.8Ti. The directionally solidified (DS) specimens of the Ti-rich alloys display higher strength compared to the arc-melted specimens. This enhanced strength is attributed to the multiple precipitation strengthening events present, despite the increase in the length scale of individual phases which further enhances the fracture toughness.

Thermal and Mechanical Mechanisms of Polymer Wear at the Nanoscale.

Wear is a ubiquitous phenomenon that limits the life of many engineered components with sliding interfaces through the gradual removal of material. The wear of polymers is crucial in many applications, ranging from bearings to orthopedic implants to nanolithography processes. The wear rate of polymers is strongly affected by the stress and temperature at the interface. The effects of temperature and stress are often described empirically since the wear process involves complex interactions between multiple asperities on rough surfaces over a range of length scales. Nanoscale tribology experiments at the single-asperity level have provided new insights into the underlying mechanisms of wear. Experiments on hard covalently bonded materials, including silicon and diamond, have demonstrated that wear is an atomic attrition wear process that can be modeled using stress-assisted transition state theory. Here, we examine the wear of a common polymer, polymethylmethacrylate (PMMA), at the nanoscale as a function of stress and temperature and show that the polymer wear is controlled by a combination of atomic attrition and viscoelastic relaxation. While the wear experiments are conducted at the nanoscale via atomic force microscopy, the results show that accounting for the local stress distribution at the contact interface is critical to understanding the wear behavior, an effect that was not considered in earlier studies on hard materials. Using a model that accounts for the stress distribution, we demonstrate the ability to predict the wear volume within 8%.

Compensating for the corolla? Pollen exposure is not associated with pollen collecting hair length.

Secondary pollen-presentation, the relocation of pollen from the anthers to elsewhere on the flower, has evolved multiple times across many plant families. While hypotheses suggest it evolved to promote outcrossing, a byproduct of relocation may be protection of pollen from loss due to abiotic factors. In Campanulaceae pollen is presented on pollen-collecting hairs along the style and the hairs retract over time and release pollen for transfer. Campanulaceae taxa vary in the degree to which pollen is exposed to environmental factors due to variation in the corolla shape and size. We tested the protective function of pollen-collecting hairs by assessing whether there was a tradeoff between the protection provided by the corolla and the pollen-collecting hairs. We used phylogenetic comparative methods to test for associations between pollen-collecting hair length, floral shape and size metrics, and pollen exposure traits across 39 species. We anticipated longer pollen-collecting hairs in taxa with more exposed pollen presentation but found there was no relationship between estimates of pollen exposure and pollen-collecting hair length. However, pollen-collecting hair length scaled allometrically with floral size, and variation in pollen-collecting hairs, as well as most floral traits, was phylogenetically structured. These results indicate that variation in pollen exposure across species does not structure variation in the pollen-collecting hairs, rather hair length scales allometrically and is phylogenetically constrained, therefore pollen-collecting hairs are unlikely to facilitate protection from environmental pressures.

Self-assembly of sustainable plant protein protofilaments into a hydrogel for ultra-low friction across length scales

Designing plant protein-based aqueous lubricants can be of great potential to achieve sustainability objectives by capitalising on inherent functional groups without using synthetic chemicals; however, such a concept remains in its infancy. Here, we engineer a class of self-assembled sustainable materials by using plant-based protofilaments and their assembly within a biopolymeric hydrogel giving rise to a distinct patchy architecture. By leveraging physical interactions, this material offers superlubricity with friction coefficients of 0.004-to-0.00007 achieved under moderate-to-high (102-to-103 kPa) contact pressures. Multiscale experimental measurements combined with molecular dynamics simulations reveal an intriguing synergistic mechanism behind such ultra-low friction - where the uncoated areas of the protofilaments glue to the surface by hydrophobic interactions, whilst the hydrogel offers the hydration lubrication. The current approach establishes a robust platform towards unlocking an untapped potential of using plant protein-based building blocks across diverse applications where achieving superlubricity and environmental sustainability are key performance indicators.