Hierarchy Of Length Scales Research Articles

Design optimization of integrated cooling inserts in modular Fischer-Tropsch reactors

Sustainable production of liquid fuels and feedstocks from atmospheric CO2 through carbon recycling technologies is necessary to broaden decarbonization efforts and further reduce global emissions. Fischer–Tropsch (FT) reactors can address this challenge by providing storable, high-value liquid hydrocarbon fuels and feedstocks from syngas generated through reductive CO2 utilization. FT technology, however, is most cost effective at large-scale, fixed-site plants and does not effectively address the smaller, globally distributed CO2 point sources. Alternatively, smaller, modular reactors can be composed together to the specific scale of the emission source, yielding a flexible solution that enables more widespread deployment. In these modular reactors, thermal management using a finned cooling insert embedded within the catalyst matrix is critical to maintaining the performance and viability. Thus, in this work, topology optimization is used to determine the cooling insert geometry that maximizes reactor productivity while preventing auto-thermal runaway. Optimal designs are generated for varying number of constituent fins and over a range of maximum operating temperatures. Constraints including minimum feature length-scales and prescribed cooling insert material are imposed on the designs to enhance manufacturability. The impact of design features such as insert tapering and increased length scale hierarchy is automatically revealed by the systematic design framework employed. This approach thus generates novel optimal geometries while automating, accelerating, and enhancing the design process compared to traditional heuristic approaches for cooling insert design in modular FT reactors.

Topology optimization for the design of porous electrodes

Porous electrodes are an integral part of many electrochemical devices since they have high porosity to maximize electrochemical transport and high surface area to maximize activity. Traditional porous electrode materials are typically homogeneous, stochastic collections of small-scale particles and offer few opportunities to engineer higher performance. Fortunately, recent breakthroughs in advanced and additive manufacturing are yielding new methods to structure and pattern porous electrodes across length scales. These architected electrodes are emerging as a promising new technology to continue to drive improvement; however, it is still unclear which structures to employ and few tools are available to guide their design. In this work we address this gap by applying topology optimization to the design of porous electrodes. We demonstrate our framework on two applications: a porous electrode driving a steady Faradaic reaction and a transiently operated electrode in a supercapacitor. We present computationally designed electrodes that minimize energy losses in a half-cell. For low-conductivity materials, the optimization algorithm creates electrode designs with a hierarchy of length scales. Further, the designed electrodes are found to outperform undesigned, homogeneous electrodes. Finally, we present three-dimensional porous electrode designs. We thus establish a topology optimization framework for designing porous electrodes.

Light scattering from colloidal aggregates on a hierarchy of length scales.

Disordered dielectrics with structural correlations on length scales comparable to visible light wavelengths exhibit interesting optical properties. Such materials exist in nature, leading to beautiful structural non-iridescent color, and they are also increasingly used as building blocks for optical materials and coatings. In this article, we explore the angular resolved single-scattering properties of micron-sized, disordered colloidal assemblies. The aggregates act as structurally colored supraparticles or as building blocks for macroscopic photonic glasses. We obtain first experimental data for the differential scattering and transport cross-section. Based on existing macroscopic models, we develop a theoretical framework to describe the scattering from densely packed colloidal assemblies on a hierarchy of length scales.

Direct measurements of the microstructural origin of shear-thinning in carbon black suspensions

Scientific questions surrounding the shear-dependent microstructure of carbon black suspensions are motivated by a desire to predict and control complex rheological and electrical properties encountered under shear. In this work, direct structural measurements over a hierarchy of length scales spanning from nanometers to tens of micrometers are used to determine the microstructural origin of the suspension viscosity measured at high shear rates. These experiments were performed on a series of dense suspensions consisting of high-structured carbon blacks from two commercial sources suspended in two Newtonian fluids, propylene carbonate and light mineral oil. The shear-induced microstructure was measured at a range of applied shear rates using Rheo-VSANS (very small angle neutron scattering) and Rheo-USANS (ultra-small angle neutron scattering) techniques. A shear-thinning viscosity is found to arise due to the self-similar break up of micrometer-sized agglomerates with increasing shear intensity. This self-similarity yields a master curve for the shear-dependent agglomerate size when plotted against the Mason number, which compares the shear force acting to break particle-particle bonds to the cohesive force holding bonds together. It is found that the agglomerate size scales as R g , agg ∼ M n − 1. Inclusion of the particle stress contribution extends the relevance of the Mason number to concentrated suspensions such as those relevant to the processing of carbon black suspensions for various applications.

Hubbard ladders at small U revisited

We re-examine the zero temperature phase diagram of the two-leg Hubbard ladder in the small $U$ limit, both analytically and using density-matrix renormalization group (DMRG). We find a ubiquitous Luther-Emery phase, but with a crossover in behavior at a characteristic interaction strength, $U^\star$; for $U \gtrsim U^\star$, there is a single emergent correlation length $\log[\xi] \sim 1/U$, characterizing the gapped modes of the system, but for $U\lesssim U^\star$ there is a hierarchy of length scales, differing parametrically in powers of $U$, reflecting a two-step renormalization group flow to the ultimate fixed point. Finally, to illustrate the versatility of the approach developed here, we sketch its implications for a half-filled triangular lattice Hubbard model on a cylinder, and find results in conflict with inferences concerning the small $U$ phase from recent DMRG studies of the same problem.

High-speed x-ray phase contrast imaging and digital image correlation analysis of microscale shock response of an additively manufactured energetic material simulant

The performance of energetic materials subjected to dynamic loading significantly depends on their micro- and meso-scale structural morphology. The geometric versatility offered by additive manufacturing opens new pathways to tailor the performance of these materials. Additively manufactured energetic materials (AMEMs) have a wide range of structural characteristics with a hierarchy of length scales and process-inherent heterogeneities, which are hitherto difficult to precisely control. It is important to understand how these features affect AMEMs’ response under dynamic/shock loading. Therefore, temporally and spatially resolved measurements of both macroscopic behavior and micro- and meso-level processes influencing macroscopic behavior are required. In this paper, we analyze the shock compression response of an AMEM simulant loaded under several impact conditions and orientations. X-ray phase contrast imaging (PCI) is used to track features across the observed shock front and determine the linear shock velocity vs particle velocity equation of state, as well as to quantify the interior deformation fields via digital image correlation (DIC) analyses. Photon Doppler velocimetry is simultaneously used to measure the particle velocities of the specimens, which are consistent with those obtained from x-ray PCI. The DIC analyses provide an assessment of the average strain fields inside the material, showing that the average axial strain depends on the loading intensity and reaches as high as 0.23 for impact velocities up to 1.5 km/s. The overall results demonstrate the utility of x-ray PCI for probing “in-material” equation of state and interior strains associated with dynamic shock compression behavior of the AMEM simulant.

Pore-Scale Modeling of the Fuel Cell Catalyst Layer: The Role of Nafion Thin Films

In this work, a multiphysics pore-scale model of electrochemical reactive transport inside a fuel cell catalyst layer (CL) is presented and is used to elucidate the role of Nafion thin films on the overall performance of the CL. One of the main challenges of modeling transport in CL is the hierarchy of length scales and the multiphysics nature of transport. Consequently, traditional continuum methods, in which volume-averaged quantities are used to encapsulate the microstructural features, cannot give a clear picture of the multiphysics transport processes inside the CL. Alternatively, pore-scale methods, which take into account the true geometry down to the pore level, are suited to capture these processes for such systems. Previously, researchers have mainly employed direct numerical simulation (DNS) techniques for pore-scale modeling of the CL. While these techniques are highly accurate, they are very computationally expensive. This limits the domain size that can be simulated in a reasonable time. In this work, pore network modeling, a computationally cheap technique to simulate pore-scale transport, is used to study transport in the CL. Using this approach, we were able to speed up the simulation runtime up to 20-50x compared to DNS. Consequently, simulation of much larger domains of the CL was made possible, leading to more representative results. Finally, the developed multiphysics pore-scale model was used to study the role of Nafion thin films on the overall performance of the CL. It is notable that the network approach was only applied to the void phase, and the Nafion region was resolved using DNS. Therefore, yet further speed up can potentially be obtained by applying the network approach to the Nafion phase.

Spontaneous formation of thermodynamically stable Al-Cu-Fe icosahedral quasicrystal from realistic atomistic simulations

Icosahedral quasicrystals spontaneously form from the melt in simulations of Al--Cu--Fe alloys. We model the interatomic interactions using oscillating pair potentials tuned to the specific alloy system based on a database of density functional theory (DFT)-derived energies and forces. Favored interatomic separations align with the geometry of icosahedral motifs that overlap to create face-centered icosahedral order on a hierarchy of length scales. Molecular dynamics simulations, supplemented with Monte Carlo steps to swap chemical species, efficiently sample the configuration space of our models, which reach up to 9846 atoms. Exchanging temperatures of independent trajectories (replica exchange) allows us to achieve thermal equilibrium at low temperatures. By optimizing structure and composition we create structures whose DFT energies reach to within $\sim$2 meV/atom of the energies of competing crystal phases. Free energies obtained by adding contributions due to harmonic and anharmonic vibrations, chemical substitution disorder, phasons, and electronic excitations, show that the quasicrystal becomes stable against competing phases at temperatures above 600K. The average structure can be described succinctly as a cut through atomic surfaces in six-dimensional space that reveal specific patterns of preferred chemical occupancy. Atomic surface regions of mixed chemical occupation demonstrate the proliferation of phason fluctuations, which can be observed in real space through the formation, dissolution and reformation of large scale icosahedral motifs -- a picture that is hidden from diffraction refinements due to averaging over the disorder and consequent loss of information concerning occupancy correlations.

Topology of transition metal dichalcogenides: the case of the core-shell architecture.

Non-planar architectures of the traditionally flat 2D materials are emerging as an intriguing paradigm to realize nascent properties within the family of transition metal dichalcogenides (TMDs). These non-planar forms encompass a diversity of curvatures, morphologies, and overall 3D architectures that exhibit unusual characteristics across the hierarchy of length-scales. Topology offers an integrated and unified approach to describe, harness, and eventually tailor non-planar architectures through both local and higher order geometry. Topological design of layered materials intrinsically invokes elements highly relevant to property manipulation in TMDs, such as the origin of strain and its accommodation by defects and interfaces, which have broad implications for improved material design. In this review, we discuss the importance and impact of geometry on the structure and properties of TMDs. We present a generalized geometric framework to classify and relate the diversity of possible non-planar TMD forms. We then examine the nature of curvature in the emerging core-shell architecture, which has attracted high interest due to its versatility and design potential. We consider the local structure of curved TMDs, including defect formation, strain, and crystal growth dynamics, and factors affecting the morphology of core-shell structures, such as synthesis conditions and substrate morphology. We conclude by discussing unique aspects of TMD architectures that can be leveraged to engineer targeted, exotic properties and detail how advanced characterization tools enable detection of these features. Varying the topology of nanomaterials has long served as a potent methodology to engineer unusual and exotic properties, and the time is ripe to apply topological design principles to TMDs to drive future nanotechnology innovation.

Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

The abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the abelian Higgs model with $n$ complex scalar fields at unprecedented four-loop order in the $4-\epsilon$ expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of $n_c \approx 182.95\left(1 - 1.752\epsilon + 0.798 \epsilon^2 + 0.362\epsilon^3\right) + \mathcal{O}\left(\epsilon^4\right)\nonumber$. Consequently, below $n_c$, the transition turns from second to first order. Resummation of the series to extract the result in three-dimensions provides strong evidence for a critical $n_c(d=3)$ which is significantly below the leading-order value, but the estimates for $n_c$ are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for $n_c(d)$ and find $n_c(3)\approx 12.2\pm 3.9$ as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below $n_c$ and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different $n$.

A finite element approach to forward modeling of nuclear magnetic resonance measurements in coupled pore systems.

Porous media characterized by a hierarchy of length scales are ubiquitous in industry and nature, and include carbonate rocks, cements, heterogeneous catalysts, and biological cells. Nuclear magnetic resonance (NMR) is a popular tool for studying liquid-saturated porous materials, where the spin relaxation rate is generally considered proportional to pore size. However, in porous granular media, the relaxation rate is modified by diffusion between the intraparticle and interparticle pores. The observed relaxation rates do not reflect the pore size under such conditions. Deconvolving the various contributions of surface relaxation, geometry, and diffusion is nontrivial, and forward models are a powerful technique for elucidating the underlying pore structure. Various forward models have been proposed previously, including analytic solutions and random walk simulations. Here, a finite element method is adopted to simulate the diffusion of nuclear magnetization in a coupled pore geometry. We validate our model against existing solutions and use the simulations to determine the surface relaxivity of powdered silica by matching experimental results. The finite element approach is more versatile than other modeling methods, allowing direct visualization of the diffusing magnetization and being trivially extensible to multidimensional NMR exchange experiments.

Measuring cosmic distances with standard sirens

The gravitational waves accompanying the merger of two massive compact objects encode the distance to the merger without the usual appeal to a hierarchy of length scales.

Coexistence of adjacent vacancy-ordered and eutectic phases in Al–Cu–Ni alloys

ABSTRACTCopper-mould-cast Al–Cu–Ni alloys show adjacent coexistence of in situ grown ordered and eutectic phases. A bimodal microstructure of α–Al and eutectic α-Al+θ-Al2Cu phases with length-scale hierarchy evolves during solidification. Microstructural analysis through Transmission Electron Microscopy (TEM) and Scanning Electron Microscopy (SEM) shows the presence of Vacancy-ordered phases (VOPs) with different morphologies in two different compositions.

Numerical inversion methods for recovering negative amplitudes in two-dimensional nuclear magnetic resonance relaxation-time correlations

Two-dimensional nuclear magnetic resonance measurements are ubiquitous in the literature, with correlations of longitudinal ${T}_{1}$ and transverse ${T}_{2}$ relaxation times used extensively to characterize porous media. Decomposition of the signal acquired in the time domain to a pseudocontinuous distribution of relaxation times is achieved using numerical inversion. A popular technique to generate a stable solution to this ill-posed problem in the presence of noise is Tikhonov regularization with a non-negativity constraint imposed on the output. However, coupling of the longitudinal and transverse eigenfunctions can generate eigenvalue pairs with apparent ${T}_{2}g{T}_{1}$ and negative amplitude. Such apparent signal components are encountered in the classic example of Brownstein-Tarr ``slow'' diffusion in an isolated pore, and in weakly coupled pores governed by different relaxation rates. We show that when negative-amplitude components comprise $\ensuremath{\ge}1%$ of the total signal, the solution achieved by non-negative Tikhonov regularization is sufficiently distorted to prevent robust interpretation. We demonstrate two alternative inversion methods that recover the negative-amplitude components: (1) half-bound Tikhonov regularization assigns a negative amplitude to any peak with apparent ${T}_{2}g{T}_{1}$, and (2) the optimization problem is expressed as a ${\ensuremath{\ell}}_{2}$ regression with ${\ensuremath{\ell}}_{1}$ penalization and a solution estimated using a primal-dual algorithm without constraint on the output sign. These methods are applicable to ${T}_{1}\ensuremath{-}{T}_{2}$ experiments on porous materials characterized by a hierarchy of length scales, such as biological cells, cement, and limestone.

Elastic Fluctuations and Structural Heterogeneities in Metallic Glasses

AbstractSuppressing crystallization of a metallic melt results in a disordered solid, also known as a metallic glass. One may conclude that a metallic glass is free of defined structural length scales beyond some atomic‐scale value that characterizes short‐ and medium‐range order. While it is well known from atomistic modeling that a metallic glass is structurally heterogeneous, heterogeneities at such a small length scale can hardly be resolved in experiments. This review highlights experimental insights into elastic fluctuations and structural heterogeneities that emerge at scales between a few nanometers and tens to hundreds of micrometers. It distinguishes between structural and property fluctuations in as‐cast metallic glasses, and heterogeneities introduced by elastic and inhomogeneous plastic deformation. As‐cast glasses reveal elastic fluctuations across 3 orders of magnitude, suggesting a hierarchy of length scales that can be tuned by thermomechanical processing. Similarly, nanoscale strain localization into shear bands drives the formation of structural and elastic heterogeneities at both the nano‐ and the microscale. It is proposed that both types of fluctuations will allow one to quantitatively define structure–property relationships via measurable length scales—an approach that has largely contributed to the engineering success of crystalline metals.

Molecular Grammar Governing Phase Behavior of Intrinsically Disordered Proteins with Prion-like Domains

There is growing interest in uncovering the rules that govern the sequence-determinants of phase separation of intrinsically disordered proteins (IDPs). This has direct relevance for reversible formation/dissociation of membraneless organelles and other biomolecular condensates. Here, we focus on a subset of IDPs with prion-like domains (PLDs) whose phase behavior appears to be governed by a rather simple molecular grammar. To the first order, IDPs with PLDs can be reduced to a flexible polymer chain comprising multiple interacting motifs connected by spacers. The minimal motifs are individual amino acids, specifically tyrosine and arginine. We present a mean-field theory that predicts critical concentrations for phase separation as a function of Tyr/Arg motif numbers. The theory, which was tested in numerical lattice simulations, provides a first-order explanation for experimentally measured critical concentrations of a family of IDPs with PLDs. Interestingly, substitutions of Tyr with Phe or Arg with Lys residues drastically weakens the driving forces for phase separation, suggesting that the grammar cannot be simply reduced to the multivalency of cation-pi interactions. Instead, phase separation requires collective interactions amongst a multiplicity of Tyr/Arg motifs that implies involvement of a hierarchy of length scales and orientational effects. Finally, spacers interspersed between the Tyr/Arg motifs serve as secondary modulators of the driving forces for phase separation and as primary determinants of the material properties, specifically the fluidity of droplets. Here too, the choice of optimal spacers is non-random, with a decided preference for Gly residues, which promotes inter-chain overlaps that appear to promote collective interactions. The combined experimental and theoretical analysis enables proteome-wide predictions of critical concentrations of disordered regions with Tyr/Arg motifs and begins to open the door to designing sequences with bespoke phase behavior.

AFM-Nanomechanical Test: An Interdisciplinary Tool That Links the Understanding of Cartilage and Meniscus Biomechanics, Osteoarthritis Degeneration, and Tissue Engineering.

Our objective is to provide an in-depth review of the recent technical advances of atomic force microscopy (AFM)-based nanomechanical tests and their contribution to a better understanding and diagnosis of osteoarthritis (OA), as well as the repair of tissues undergoing degeneration during OA progression. We first summarize a range of technical approaches for AFM-based nanoindentation, including considerations in both experimental design and data analysis. We then provide a more detailed description of two recently developed modes of AFM-nanoindentation, a high-bandwidth nanorheometer system for studying poroviscoelasticity and an immunofluorescence-guided nanomechanical mapping technique for delineating the pericellular matrix (PCM) and territorial/interterritorial matrix (T/IT-ECM) of surrounding cells in connective tissues. Next, we summarize recent applications of these approaches to three aspects of joint-related healthcare and disease: cartilage aging and OA, developmental biology and OA pathogenesis in murine models, and nanomechanics of the meniscus. These studies were performed over a hierarchy of length scales, from the molecular, cellular to the whole tissue level. The advances described here have contributed greatly to advancing the fundamental knowledge base for improved understanding, detection, and treatment of OA.

Toward Understanding the Environmental Control of Hydrogel Film Properties: How Salt Modulates the Flexibility of Chitosan Chains

Chitosan is a pH-responsive self-assembling polysaccharide that can be electrodeposited to form a hydrogel film. During electrodeposition a host of dynamic processes occur simultaneously over a hierarchy of length scales. Experiments have shown that the microstructure and properties of the deposited gels are highly dependent on the solution conditions and imposed electrical signals. However, detailed mechanisms are not understood. Here we use molecular dynamics simulations to explore the conformational dynamics of individual chitosan chains composed of 20 glucosamine units in aqueous solution. Simulations yield a total persistence length of about 5 nm, in agreement with the lower range of the experimental estimates and supporting a worm-like-chain model. The surprisingly high flexibility arises from the glycosidic linkage sampling an appreciable population of anti-ψ conformation which is associated with backbone bending and higher flexibility. Significantly, the presence of added salt increases the anti-ψ...

Helium Nanobubbles Enhance Superelasticity and Retard Shear Localization in Small-Volume Shape Memory Alloy.

The intriguing phenomenon of metal superelasticity relies on stress-induced martensitic transformation (SIMT), which is well-known to be governed by developing cooperative strain accommodation at multiple length scales. It is therefore scientifically interesting to see what happens when this natural length scale hierarchy is disrupted. One method is producing pillars that confine the sample volume to micrometer length scale. Here we apply yet another intervention, helium nanobubbles injection, which produces porosity on the order of several nanometers. While the pillar confinement suppresses superelasticity, we found the dispersion of 5-10 nm helium nanobubbles do the opposite of promoting superelasticity in a Ni53.5Fe19.5Ga27 shape memory alloy. The role of helium nanobubbles in modulating the competition between ordinary dislocation slip plasticity and SIMT is discussed.

Plasticity performance of Al0.5CoCrCuFeNi high-entropy alloys under nanoindentation

The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy, Al0.5 CoCrCuFeNi, were analyzed for the nanoindentation performed at two temperatures. Critical behavior of serrations at room temperature and chaotic flows at 200 °C were detected. These results are attributed to the interaction among a large number of slip bands. For the nanoindentation at room temperature, recurrent partial events between slip bands introduce a hierarchy of length scales, leading to a critical state. For the nanoindentation at 200 °C, there is no spatial interference between two slip bands, which is corresponding to the evolution of separated trajectory of chaotic behavior.