Distinct Length Scales Research Articles

Two Diverging Length Scales in the Structure of Jammed Packings.

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ_{Z}, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, ξ_{f}, is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ_{f}, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ_{Z} and ξ_{f} are different and appear to be different in two and three dimensions.

Compressive behavior and failure mechanisms of freestanding and composite 3D graphitic foams

Open-cell graphitic foams were fabricated by chemical vapor deposition using nickel templates and their compressive responses were measured over a range of relative densities. The mechanical response required an interpretation in terms of a hierarchical micromechanical model, spanning 3 distinct length scales. The power law scaling of elastic modulus and yield strength versus relative density suggests that the cell walls of the graphitic foam deform by bending. The length scale of the unit cell of the foam is set by the length of the struts comprising the cell wall, and is termed level I. The cell walls comprise hollow triangular tubes, and bending of these strut-like tubes involves axial stretching of the tube walls. This length scale is termed level II. In turn, the tube walls form a wavy stack of graphitic layers, and this waviness induces interlayer shear of the graphitic layers when the tube walls are subjected to axial stretch. The thickness of the tube wall defines the third length scale, termed level III. We show that the addition of a thin, flexible ceramic Al2O3 scaffold stiffens and strengthens the foam, yet preserves the power law scaling. The hierarchical model gives fresh insight into the mechanical properties of foams with cell walls made from emergent 2D layered solids.

Structure, Properties, and Degradation of Nanothin Ionomer Films in Fuel Cell Catalytic Layers

The structure of electrodes for proton-exchange membrane fuel cells and electrolysis has a major impact on performance and degradation. Ionomer films covering Pt/C agglomerates in fuel cell electrodes have a thickness in the range of 4 to 15 nm. Such nanothin ionomer films differ significantly in structure and conductivity from bulk ionomer To access their thickness-structure-conductivity correlations, self-assembled model layers deposited on platinum-covered Si were investigated by material-sensitive and conductive AFM at conditions close to operation. The dependence of transient current on ionomer film height measured directly at samples with a varying thickness has two distinct changes of slope which indicates three distinct length scales (< 4-5 nm, ~ 4-8 nm, > 8 nm) over which structure and subsequently the conductivity of nanothin films varies.

Hierarchical micromechanical modeling of the viscoelastic behavior coupled to damage in SMC and SMC-hybrid composites

Abstract The aim of this paper is to study, through a multiscale analysis, the viscoelastic behavior of glass reinforced sheet molding compound (SMC) composites and SMC-hybrid composites mixing two types of bundle reinforcement: glass and carbon fibers. SMC exhibit more than two distinct characteristic length scales, so that a sequence of scale transitions is required to obtain the overall behavior of the composite. An analytical procedure is used consisting of properly selected well-established micromechanical methods like the Mori-Tanaka (MTM) and the composite cylinders (CCM) accounting for each scale transition. After selecting a representative volume element (RVE) for each scale, the material response of any given length scale is described on the basis of the homogenized behavior of the next finer one. This hierarchical approach is appropriately extended to the viscoelastic domain to account for the time dependent overall response of the SMC composite material. The anisotropic damage has been introduced through a micromechanical model considering matrix penny-shape microcrack density inside bundles. The capabilities of the hierarchical modeling are illustrated with various parametric studies and simulation of experimental data for glass-based SMC composites.

Disordered dipolar solids: Anisotropic growth laws and their slowing-down

We use Monte Carlo simulations to study the kinetics of domain growth in the d = 3 random-field Ising model with dipolar interactions (RFIM+DI). This system models a large class of magnetic and dielectric solids. Our main results are as follows: i) The domains are anisotropic and elongated along the Ising (z) axis. The system exhibits generalized dynamical scaling with two distinct length scales and , where . However, the scaling function is not robust with respect to the disorder Δ. ii) For a fixed value of Δ, the interfaces are fractal with distinct fractal dimensions in the xy-plane and the z-direction. iii) The domain growth laws are also anisotropic, and exhibit distinct power laws on the time-scales of our simulations: and . iv) The exponents and have a simple dependence on Δ. Our results are novel and provide a fresh outlook to interpret experiments in disordered dipolar solids.

Role of low-temperature chemistry in detonation of n-heptane/oxygen/diluent mixtures

The ZND structure of mixtures of n-heptane, oxygen and diluent has been investigated using a reduced reaction scheme that includes the low-temperature chemistry (LTC) pathways. It is shown that for high CO2 contents (XCO2 > 0.82) such that the reaction temperature is relatively low, the structure is affected by LTC and exhibits two distinct stages of energy release caused by low- and high-temperature chemistry, respectively. Based on the ZND structures, the dynamic parameters such as cell size, direct initiation energy and critical tube diameter of detonation within the LTC affected regime have been evaluated using various semi-empirical models. Such detonation structures exhibiting two distinct length scales lead to two distinct values for each of these dynamic parameters. For the evolution of the induction length and cell size, although the total length scales do not show negative response with increasing temperature, the length scale of the first-stage ignition demonstrates negative response when the post-shock temperature decreases within the LTC controlled regime. For the evolution of direct initiation energy, the models based on critical curvature and critical decay rate show negative temperature response, but the model based on cell size predicts continuous increase of critical initiation energy with increasing dilution. For the critical tube diameter, the model based on the critical decay rate approach also exhibits the negative temperature response.

Evidence for the role of the magnon energy relaxation length in the spin Seebeck effect

Temperature-dependent spin Seebeck effect data on Pt|yttrium iron garnet (YIG) (${\mathrm{Y}}_{3}\mathrm{F}{\mathrm{e}}_{5}{\mathrm{O}}_{12}$)|gallium gadolinium garnet ($\mathrm{G}{\mathrm{d}}_{3}\mathrm{G}{\mathrm{a}}_{5}{\mathrm{O}}_{12}$) are reported for YIG films of various thicknesses. The effect is reported as a spin Seebeck resistivity (SSR), the inverse spin-Hall field divided by the heat flux, to circumvent uncertainties about temperature gradients inside the films. The SSR is a nonmonotonic function of YIG thickness. A diffusive model for magnon transport demonstrates how these data give evidence for the existence of two distinct length scales in thermal spin transport, a spin-diffusion length, and a magnon energy relaxation length.

Turbulent jet from a slender annular slot ventilated by a self-induced flow through the open core

The dynamics of an incompressible turbulent air jet from an annular source into otherwise quiescent surroundings are investigated. Focussing on a slender annulus with an open core, the development of the jet is examined using planar and stereoscopic particle image velocimetry (PIV) from the source to 16 (outer) source diameters downstream. Unique to these annular sources, the jet induces a flow through the open core - in other words, the core is `ventilated'. Our measurements indicate that the volume flux drawn through the core exceeds that from the source by approximately 20%. Based on the streamwise development of the jet, we identify four distinct regions: (i) an internal region of induced flow that is bounded by the jet; (ii) a near-field planar-jet-like region; (iii) a transition region; and, ultimately, (iv) a far- field round-jet-like region. We explore the evolution of the jet towards self-similar behaviour based on cross-stream profiles of time-averaged velocity and turbulence statistics within these different regions. Four distinct length scales are shown to characterise the streamwise extents and behaviours within the regions identified. Finally, to highlight the role of the open-core (ventilated) annular geometry on jet development, comparisons are made with PIV measurements of turbulent jets issuing from circular sources. These comparisons reveal that the ventilated geometry significantly enhances dilution in the near field.

Investigating Novel Anion-Conducting Polymers Via X-Ray Scattering

Hexamethyl-p-terphenyl poly(benzimidazolium) (HMT-PMBI) is a hydroxide-resistant, high-performing anion-conducting polymer. Such materials are very interesting, as they may allow the use of hydrogen fuel cells without platinum-group catalysts [1]. We have investigated the structure of this material using small-angle x-ray scattering (SAXS,) small-angle neutron scattering (SANS,) and computational methods. Our SAXS results revealed three distinct length scales, which we assigned to ion-polymer, interchain, and monomer length scales. A molecular dynamics (MD) simulation reproduced these features of the scattering curve and corroborated our interpretations of them. No structure at larger length scales was observed; the lack of large watery regions, common in high-performance ion-exchange membranes, may contribute to the material’s remarkable mechanical stability. [1] A.G. Wright and S. Holdcroft, ACS Macro Lett. 3, 444 (2014). Figure 1

A new model for flow in shale-gas reservoirs including natural and hydraulic fractures

In this work, we construct a new coupled Multiscale/Discrete Fracture Model for compressible flow in a multiporosity shale gas reservoir containing networks of natural and hydraulic fractures. The geological formation is characterized by four distinct length scales and levels of porosity. The window of observation of the finest (nanoscale) portraits the nanopores within organic matter containing adsorbed gas. At the microscale, the medium is formed by two solid phases: organic, composed by kerogen aggregates, and inorganic (clay, quartz, calcite). Such phases are separated by the network of partially-saturated interparticle pores where microscopic free gas flow influenced by Knudsen effects along with gas diffusion in the immobile water phase occur simultaneously. The upscaling of the local flow to the mesoscale gives rise to a nonlinear homogenized pressure equation in the shale matrix which lies adjacent to the system of natural fractures. Homogenization of the coupled matrix/preexisting fractures to the macroscale leads to a microstructural model of dual porosity type. Such homogenized model is subsequently coupled with the hydrodynamics in the network of induced fractures which, in the context of the discrete fracture modeling, are treated as (n − 1), (n = 2, 3) lower dimensional objects. In order to handle numerically the nonlinear interaction between the different flow equations, we adopt a superposition argument, firstly proposed by Arbogast (1996), in each iteration of a fixed-point algorithm. The resultant governing equations are discretized by the finite element method and numerical simulations of gas production in stratified arrangements of the fracture networks are presented to illustrate the potential of the multiscale approach.

Scaling Equation for Viscosity of Polymer Mixtures in Solutions with Application to Diffusion of Molecular Probes

We measured macroscopic viscosity as well as nanoviscosity experienced by molecular probes diffusing in solutions containing two polymer species vastly differing in the molecular weight. On this basis we postulated a scaling equation for viscosity of complex liquids characterized by two distinct length-scales. As an experimental model, we used aqueous solutions of low-polydispersity poly(ethylene glycol) and poly(ethylene oxide) with molecular weight ranging from 6 to 1000 kg/mol, polymer concentrations from 0.25% up to 50%, and viscosity up to 500 mPa·s. The proposed model distinguishes between the contributions to the total viscosity stemming from the mesoscopic structure of the complex liquid and from the magnitude of interactions dictated by the chemical nature of its constituents. It allows to predict diffusion rates of nanoscaled probes in polymer solution mixtures and can be adapted to various multilength-scale complex systems.

Lattice Models for Modeling Sequence-Specific Phase Behavior of Low Complexity Domains

Low complexity domains (LCDs), enriched in charged, polar, and aromatic residues are drivers of aggregation and phase separation in a variety of proteins including those that drive the formation of RNA-protein granules. Polyglutamine (polyQ) tracts are a distinct archetype of LCDs. Mutational expansion of polyQ tracts in specific proteins is associated with onset and progression of at least nine different neurodegenerative disorders including Huntington's disease. The latter is associated with an expanded polyQ tract in the protein huntingtin. Recent experiments have uncovered complex thermodynamic and kinetic phase diagrams for N-terminal fragments of huntingtin. These phase diagrams are modulated by polyQ length, sequence contexts, concentration, and solution conditions. The details of the molecular and supramolecular interactions that give rise to emergent phase behavior of polyQ containing at distinct length scales remains poorly understood. Computations play an important role in predicting the phase behavior of LCDs. These calculations require simulations encompassing several hundreds of thousands of protein molecules spanning several orders of magnitude in protein concentrations. Such simulations are beyond the scope of all atom models. Since phase behavior results from the synergistic interactions amongst small numbers of collective coordinates, simulations designed to uncover sequence-encoded phase behavior can be pursued using either systematic coarse-graining or phenomenological models. Recent work has demonstrated the utility of both approaches. However, these models lack the requisite molecular detail to enable a complete understanding of sequence-specific contributions that determine similarities and differences in sequence-encoded phase behavior of LCDs. Here we present a lattice model that is tailored for modeling sequence-specific phase behaviors of LCDs. The model serves as an intermediate description between ultra coarse-graining and all-atom extremes. In the lattice model, a single bead on a 3-dimensional lattice site describes each residue. Each bead has multiple faces and this helps us capture the directionality of backbone hydrogen bonding and sidechain-specific interactions. Monte Carlo simulations based on these lattice models help us uncover the interplay amongst different sequence-encoded energy scales and phase behaviors of LCDs with polyQ tracts. Specifically, we focus on explaining the role of spherical mesophases as mediators of fibril formation in polyQ containing proteins. We also show that the model can be deployed for understanding the interplay amongst liquids, fibrils, and gels for other LCDs.

DNA ionogel: Structure and self-assembly.

DNA dissolved in ionic liquid (IL) solution (1-ethyl-3-methylimidazolium chloride, [C2mim][Cl]) showed a transition to the gel phase ([DNA] ≥ 1% (w/v)). The gelation time was 400 s for the 1% [IL] sample which reduced to 260 s for 5% [IL] concentration. Gelation times, obtained from the viscosity and ergodicity breaking from the dynamic structure factor data, were remarkably identical to each other. Correspondingly, the gelation temperature which was ∼60 °C increased to 67 °C with [IL] content. The small angle neutron scattering (SANS) structure factor profile revealed the presence of the following three distinct length scales: (a) mesh size, ξ ≈ 3 ± 0.5 nm for ionogels, and ≈0.73 ± 0.06 nm, for sol; (b) cross-sectional radius of DNA strand, Rc ≈ 1.6 ± 0.1 nm; and (c) the characteristic inter-cluster distance ≈33 ± 5 nm. Physical conformation of the DNA-IL complexes remained close to the Gaussian coil definition. It was observed that without IL, in the sol phase, the system was completely ergodic and did not gel, while on addition of IL a sudden transition to the non-ergodic (arrested) gel phase occurred. This was due to the formation of an amorphous network of DNA-IL complexes preceding gelation. In summary, it is shown that the DNA ionogels can be prepared with a tunable gel strength (27-70 Pa) and gelation temperature (60-67 °C). Further, the relaxation dynamics was found to be hierarchical in IL content of the gel, revealing considerable self-organization.

What is the “active layer”?

AbstractWe note the presence in the literature of two different concepts of the term “active layer” in relation to fluvial sediment transport. It has been used to represent the current dynamically active streambed surface, or to represent the depth of event‐scale scour and fill. These concepts involve distinct length and time scales. We propose that, when the distinction is important, the concepts be distinguished as either a “dynamical active layer” or an “event active layer.”

Effects of radial electric field on suppression of electron-temperature-gradient mode through multiscale nonlinear interactions

Turbulence in fluids and plasmas is ubiquitous in Nature and in the laboratory. Contrary to the importance of the ‘scale-free’ nature of cascade in neutral fluid turbulence, the turbulence in plasma is characterised by dynamics of distinct length scales. The cross-scale interactions can be highly non-symmetric so as to generate the plasma turbulence structures. Here we report that the system of hyper-fine electron-temperature-gradient (ETG) fluctuations and microscopic drift-wave (DW) fluctuations is strongly influenced by the sign of the gradient of the radial electric field through multiscale nonlinear interactions. The selective suppression effects by radial electric field inhomogeneity on DW mode induce a new route to modify ETG mode. This suppression mechanism shows disparity with respect to the sign of the radial electric field inhomogeneity, which can be driven by turbulence, so that it could be a new source for symmetry breaking in the turbulence structure formation in plasmas.

Monodisperse hollow silica spheres: An in-depth scattering analysis

Herein, we fabricate hollow silica nanoparticles with exceptionally narrow size distributions that inherently possess two distinct length scales—tens of nanometers with regards to the shell thickness, and hundreds of nanometers in regards to the total diameter. We characterize these structures using dynamic and static light scattering (DLS and SLS), small angle X-ray scattering (SAXS), and transmission electron microscopy (TEM), and we demonstrate quantitative agreement among all methods. The ratio between the radius of gyration (SLS) and hydrodynamic radius (DLS) in these particles equals almost unity, corresponding to ideal capsule behavior. We are able to resolve up to 20 diffraction orders of the hollow sphere form factor in SAXS, indicating a narrow size distribution. Data from light and X-ray scattering can be combined to a master curve covering a q-range of four orders of magnitude assessing all hierarchical length scales of the form factor. The measured SLS intensity profiles noticeably change when the scattering contrast between the interior and exterior is altered, whereas the SAXS intensity profiles do not show any significant change. Tight control of the aforementioned length scales in one simple and robust colloidal building block renders these particles suitable as future calibration standards.

Small-Angle Scattering Analysis of Empty or Loaded Hierarchical Porous Materials

Small-angle scattering of X-rays (SAXS) or neutrons (SANS) is one of the few experimental methods that can in principle be used for the in situ study at the mesoscopic scale of physicochemical phenomena occurring inside nanoporous solids. However, the potential of the method is often limited by the lack of suitable data analysis methods to convert scattering data into real-space structural information. This is notably the case for most porous materials of practical interest, which exhibit a hierarchical structure with micro, meso, and macropores, with often a secondary material confined in the pores, such as in supported catalysts, as well as fuel-cell and battery materials. In the present paper, we propose a general analysis of X-ray scattering by this type of material. Assuming that each structural level is statistically independent from the others and has a distinct characteristic length scale, compact mathematical expressions are derived for the scattering of the entire hierarchical structure. The res...

Slender-ribbon theory

Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example, when a ribbon has half a twist and is bent into a circle it produces a Möbius strip. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. In this paper, we determine, asymptotically, the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical ruled surface, termed as the ribbon plane, located inside the ribbon. A numerical implementation of our derivation shows good agreement with the known hydrodynamics of long flat ellipsoids and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. We also study the asymptotic behavior of a ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how accurately the hydrodynamics of a ribbon can be effectively captured by that of a slender filament. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems.

Mesoscale Transport in Magnetite Electrodes for Lithium-Ion Batteries

In recent years, magnetite (Fe3O4) has shown promise as a lithium-ion electrode material due to its low cost, safety (non-toxic), and high theoretical capacity (926 mAh/g) [1]. The high theoretical capacity results from the close-packing, inverse spinel structure of the material. This structure also hinders rapid ion transfer, which causes the experimental capacity to deviate significantly from the theoretical value [2]. To address this issue, several authors have synthesized Fe3O4nano-crystals in attempts to minimize the path length for ion transport [3-4]. Improvements in electrochemical performance have been observed; however, the mechanisms responsible for these improvements are not well understood. A complete understanding of the physical phenomena impacting performance has been difficult to obtain due to the complexity of the battery electrodes. The electrodes are composed of blends of Fe3O4, carbon black, and a polymer binder. Due to the synthesis and fabrication processes, the electrodes contain structures across three distinct length scales (Fig. 1). The crystalline active material and bulk electrode provide structure on the nano-scale and macro-scale, respectively. In addition, the intermediate length scale (i.e., the meso-scale) contains a third structure due to the presence of agglomerates, which form as a result of nano-particle aggregation. Behavior on all three length scales must be understood in order to properly interpret electrochemical data. In this work, we seek to provide a deeper understanding of the physical and chemical processes occurring in Fe3O4electrodes through a combined experimental and mathematical approach. First, to identify which length scale (crystal, agglomerate, or bulk) has the biggest impact on mass transport, the time constants associated with mass transport at each length scale have been determined through a theoretical, dimensional analysis. These results have been compared to time constants obtained from voltage relaxation experiments. From this comparison, it has been determined that mass transport on the agglomerate scale is a significant factor. Based on these findings, a one-dimensional mathematical model of a Fe­3O4agglomerate has been developed, which assumes mass transport on the crystal and bulk scales are negligible. In the model, the Butler-Volmer equation along with lithium-intercalation relations are used to simulate the charge transfer kinetics. Changes in thermodynamic potential due to changes in the degree of lithium intercalation are accounted for by fitting experimental data to a modified Nernst equation. In addition, the mesoscale transport occurring between the aggregated nano-crystals is modeled based off of electrochemical measurements and TEM images. Good agreement is observed between the simulations and experimental data for electrochemical discharge and voltage relaxation experiments (Fig. 2). These results further confirm the validity of an agglomerate-based model for this system. Using the model, we have investigated the effects of crystallite and agglomerate size on mesoscale transport in the electrode. To facilitate these studies, the model has been expanded to account for distributions in agglomerate size, which are obtained from TEM images. The resulting simulations suggest that interpretation of electrochemical performance without an understanding of the agglomerate size distributions can lead to significant errors in the analysis. [1] S. Zhu, A. C. Marschilok, E. S. Takeuchi, G. T. Yee, G. Wang, and K. J. Takeuchi, J. Electrochem. Soc., 157 (2010) A1158. [2] M. C. Menard, K. J. Takeuchi, A. C. Marshilok, and E. S. Takeuchi, Phys. Chem. Chem. Phys., 15 (2013) 18539. [3] S. Zhu, A. C. Marschilok, E. S. Takeuchi, and K. J. Takeuchi, Electrochem. Solid-State Lett., 12 (2009) A91. [4] Z. Cui, L. Jiang, W. Song, and Y. Guo, Chem. Mat., 21 (2009) 1162. Figure 1

Length-Scale-Dependent Phase Transformation of LiFePO4 : An In situ and Operando Study Using Micro-Raman Spectroscopy and XRD.

The charge and discharge of lithium ion batteries are often accompanied by electrochemically driven phase-transformation processes. In this work, two in situ and operando methods, that is, micro-Raman spectroscopy and X-ray diffraction (XRD), have been combined to study the phase-transformation process in LiFePO4 at two distinct length scales, namely, particle-level scale (∼1 μm) and macroscopic scale (∼several cm). In situ Raman studies revealed a discrete mode of phase transformation at the particle level. Besides, the preferred electrochemical transport network, particularly the carbon content, was found to govern the sequence of phase transformation among particles. In contrast, at the macroscopic level, studies conducted at four different discharge rates showed a continuous but delayed phase transformation. These findings uncovered the intricate phase transformation in LiFePO4 and potentially offer valuable insights into optimizing the length-scale-dependent properties of battery materials.