Longer Length Scales Research Articles

Thermal Transport in One-Dimensional Electronic Fluids

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.

Microheterogeneity and CO2 Switchability of N, N-Dimethylcyclohexylamine-Water Binary Mixtures.

Binary mixtures of water and organic solvents are described as the aqueous solutions of organic solvents, which are usually spatially heterogeneous on the scale of a few molecular sizes but homogeneous on longer length scales, that is, microheterogeneity. For the water-organic solvent binary mixtures with microheterogeneity, most organic solvents are miscible with water at any ratio. Interestingly, some slightly water-miscible organic solvents can also be used to prepare binary mixtures with microheterogeneity. In this study, N, N-dimethylcyclohexylamine (DMCHA) was used to prepare binary mixtures with microheterogeneity and CO2 switchability. With the help of conductivity, Fourier-transform infrared spectroscopy, ultraviolet-visible spectroscopy, and dynamic light scattering measurements, we found that water molecules are hydrogen-bonded together to form clusters over the water content range of 9 to 27 wt %, exhibiting microheterogeneity in the binary mixture. The size of the water clusters increases slightly with increasing water content. What is more, the DMCHA-water mixtures can be reversibly split into two phases by alternate bubbling of CO2 and N2, exhibiting excellent CO2 switchability. The binary mixtures can be used as reaction media for the synthesis of CaCO3 nanoparticles. Binary mixtures with microheterogeneity can also be formed under high salinity or high temperature conditions or be prepared using other slightly water-miscible organic solvents, opening up more interesting possibilities for binary mixtures with microheterogeneity.

Textured heterogeneity in square artificial spin ice

We report evidence of spontaneous formation of a heterogeneous network of superdomains in two-dimensional square artificial spin ice nanostructures in externally applied magnetic fields. Coherent resonant soft-x-ray scattering from such textures gives rise to unique internal structure in Bragg peaks. The magnetic heterogeneity is locally disordered but has a zigzag texture at longer length scales. Our result suggests that the macroscopic magnetic texture is derived from the microscopic structure of the Dirac strings.

Self-Similarity and the Dynamics of Coarsening in Materials

Two-phase mixtures, from metallic alloys to islands on surfaces, undergo coarsening wherein the total interfacial area of the system decreases with time. Theory predicts that during coarsening the average size-scale of a two-phase mixture increases with time as t1/3 when the two-phase mixture is self-similar, or time independent when scaled by a time-dependent length. Here, we explain why this temporal power law is so robustly observed even when the microstructure is not self-similar. We show that there exists an upper limit to the length scales in the system that are kinetically active during coarsening, which we term the self-similar length scale. Length scales smaller than the self-similar length scale evolve, leading to the classical temporal power law for the coarsening dynamics of the system. Longer length scales are largely inactive, leading to a non-self-similar structure. This result holds for any two-phase mixture with a large distribution of morphological length scales.

Nature of the high-speed rupture of the two-dimensional Burridge-Knopoff model of earthquakes.

The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate- and state-dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the emergent rupture-propagation velocity is nearly constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighbouring 'asperities' observed in real, large earthquakes. Large events tend to be unilateral, with its epicentre lying at the rim of its rupture zone. The epicentre site of a large event is also located next to the rim of the rupture zone of some past event. Event-size distributions are computed and discussed in comparison with those of the corresponding one-dimensional model. The magnitude distribution exhibits a power-law behaviour resembling the Gutenberg-Richter law for smaller magnitudes, which changes over to a more characteristic behaviour for larger magnitudes. For very large events, the rupture-length distribution exhibits mutually different behaviours in one dimension and in two dimensions, reflecting the difference in the underlying geometry.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Characterizing the Surface Roughness Length Scales of Lactose Carrier Particles in Dry Powder Inhalers.

Surface roughness is well recognized as a critical physical property of particulate systems, particularly in relation to adhesion, friction, and flow. An example is the surface property of carrier particles in carrier-based dry powder inhaler (DPI) formulations. The numerical characterization of roughness remains rather unsatisfactory due to the lack of spatial (or length scale) information about surface features when a common amplitude parameter such as average roughness ( Ra) is used. An analysis of the roughness of lactose carrier particles at three different length scales, designed for specificity to the study of interactive mixtures in DPI, was explored in this study. Three Ra parameters were used to represent the microscale, intermediate scale, and macroscale roughness of six types of surface-modified carriers. Coating of micronized lactose fines on coarse carrier particles increased their microroughness from 389 to 639 nm while the macroroughness was not affected. Roller compaction at higher roll forces led to very effective surface roughening, particularly at longer length scales. Changes in Ra parameters corroborated the visual observations of particles under the scanning electron microscope. Roughness at the intermediate scale showed the best correlation with the fine particle fraction (FPF) of DPI formulations. From the range of 250 to 650 nm, every 100 nm increase in the intermediate roughness led to ∼8% increase in the FPF. However, the effect of surface roughness was greatly diminished when fine lactose (median size, 9 μm) of comparable amounts to the micronized drug were added to the formulation. The combination of roughness parameters at various length scales provided much discriminatory surface information, which then revealed the "quality" of roughness necessary for improving DPI performance.

Generic Mechanism for Pattern Formation in the Solvation Shells of Buckminsterfullerene.

Accurate description of solvation structure of a hydrophobic nanomaterial is of immense importance to understand protein folding, molecular recognition, drug binding, and many related phenomena. Moreover, spontaneous pattern formation through self-organization of solvent molecules around a nanoscopic solute is fascinating and useful in making template-directed nanostructures of desired morphologies. Recently, it has been shown using polarizable atomistic models that the hydration shell of a buckminsterfullerene can have atomically resolved ordered structure, in which C60 atomic arrangement is imprinted. In analyzing any peculiar behavior of water, traditionally, emphasis has been placed on the long-ranged and orientation-dependent interactions in it. Here, we show through molecular dynamics simulation that the patterned solvation layer with the imprints of the hydrophobic surface atoms of the buckminsterfullerene can be obtained from a completely different mechanism arising from a spherically symmetric, short-ranged interaction having two characteristic lengthscales. The nature of the pattern can be modified by adjusting solvent density or pressure. Although solute–solvent dispersion interaction is the key to such pattern formation adjacent to the solute surface, the ordering at longer lengthscale is a consequence of mutual influence of short-range correlations among successive layers. The present study thus demonstrates that the formation of such patterned solvation shells around the buckminsterfullerene is not restricted to water, but encompasses a large class of anomalous fluids represented by two-lengthscale potential.

Commentary: The promise of polymers

Commentary: The promise of polymers

Structural imaging of nanoscale phonon transport in ferroelectrics excited by metamaterial-enhanced terahertz fields

Nanoscale phonon transport is a key process that governs thermal conduction in a wide range of materials and devices. Creating controlled phonon populations by resonant excitation at terahertz (THz) frequencies can drastically change the characteristics of nanoscale thermal transport and allow a direct real-space characterization of phonon mean-free paths. Using metamaterial-enhanced terahertz excitation, we tailored a phononic excitation by selectively populating low-frequency phonons within a nanoscale volume in a ferroelectric $\mathrm{BaTi}{\mathrm{O}}_{3}$ thin film. Real-space time-resolved x-ray diffraction microscopy following THz excitation reveals ballistic phonon transport over a distance of hundreds of nm, two orders of magnitude longer than the averaged phonon mean-free path in $\mathrm{BaTi}{\mathrm{O}}_{3}$. On longer length scales, diffusive phonon transport dominates the recovery of the transient strain response, largely due to heat conduction into the substrate. The measured real-space phonon transport can be directly compared with the phonon mean-free path as predicted by molecular dynamics modeling. This time-resolved real-space visualization of THz-matter interactions opens up opportunities to engineer and image nanoscale transient structural states with new functionalities.

Similar local order in disordered fluorite and aperiodic pyrochlore structures

A major challenge to understanding the response of materials to extreme environments (e.g., nuclear fuels/waste forms and fusion materials) is to unravel the processes by which a material can incorporate atomic-scale disorder, and at the same time, remain crystalline. While it has long been known that all condensed matter, even liquids and glasses, possess short-range order, the relation between fully-ordered, disordered, and aperiodic structures over multiple length scales is not well understood. For example, when defects are introduced (via pressure or irradiation) into materials adopting the pyrochlore structure, these complex oxides either disorder over specific crystallographic sites, remaining crystalline, or become aperiodic. Here we present neutron total scattering results characterizing the irradiation response of two pyrochlores, one that is known to disorder (Er2Sn2O7) and the other to amorphize (Dy2Sn2O7) under ion irradiation. The results demonstrate that in both cases, the local pyrochlore structure is transformed into similar short range configurations that are best fit by the orthorhombic weberite structure, even though the two compositions have distinctly different structures, aperiodic vs. disordered-crystalline, at longer length scales. Thus, a material's resistance to amorphization may not depend primarily on local defect formation energies, but rather on the structure's compatibility with meso-scale modulations of the local order in a way that maintains long-range periodicity.

Hydration kinetics and morphology of cement pastes with pozzolanic volcanic ash studied via synchrotron-based techniques

This study investigates the early ages of hydration behavior when basaltic volcanic ash was used as a partial substitute to ordinary Portland cement using ultra-small-angle X-ray scattering and wide-angle X-ray scattering (WAXS). The mix design consisted of 10, 30 and 50% substitution of Portland cement with two different-sized volcanic ashes. The data showed that substitution of volcanic ash above 30% results in excess unreacted volcanic ash, rather than additional pozzolanic reactions along longer length scales. WAXS studies revealed that addition of finely ground volcanic ash facilitated calcium-silicate-hydrate related phases, whereas inclusion of coarser volcanic ash caused domination by calcium-aluminum-silicate-hydrate and unreacted MgO phases, suggesting some volcanic ash remained unreacted throughout the hydration process. Addition of more than 30% volcanic ash leads to coarser morphology along with decreased surface area and higher intensity of scattering at early-age hydration. This suggests an abrupt dissolution indicated by changes in surface area due to the retarding gel formation that can have implication on early-age setting influencing the mechanical properties of the resulting cementitious matrix. The findings from this work show that the concentration of volcanic ash influences the specific surface area and morphology of hydration products during the early age of hydration. Hence, natural pozzolanic volcanic ashes can be a viable substitute to Portland cement by providing environmental benefits in terms of lower-carbon footprint along with long-term durability.

Dislocation Interactions in Olivine Revealed by HR‐EBSD

AbstractInteractions between dislocations potentially provide a control on strain rates produced by dislocation motion during creep of rocks at high temperatures. However, it has been difficult to establish the dominant types of interactions and their influence on the rheological properties of creeping rocks due to a lack of suitable observational techniques. We apply high‐angular resolution electron backscatter diffraction to map geometrically necessary dislocation (GND) density, elastic strain, and residual stress in experimentally deformed single crystals of olivine. Short‐range interactions are revealed by cross correlation of GND density maps. Spatial correlations between dislocation types indicate that noncollinear interactions may impede motion of proximal dislocations at temperatures of 1000°C and 1200°C. Long‐range interactions are revealed by autocorrelation of GND density maps. These analyses reveal periodic variations in GND density and sign, with characteristic length scales on the order of 1–10 μm. These structures are spatially associated with variations in elastic strain and residual stress on the order of 10−3 and 100 MPa, respectively. Therefore, short‐range interactions generate local accumulations of dislocations, leading to heterogeneous internal stress fields that influence dislocation motion over longer length scales. The impacts of these short‐ and/or long‐range interactions on dislocation velocities may therefore influence the strain rate of the bulk material and are an important consideration for future models of dislocation‐mediated deformation mechanisms in olivine. Establishing the types and impacts of dislocation interactions that occur across a range of laboratory and natural deformation conditions will help to establish the reliability of extrapolating laboratory‐derived flow laws to real Earth conditions.

Effects of anisotropic turbulent thermal diffusion on spherical magnetoconvection in the Earth’s core

We re-consider the plate-like model of turbulence in the Earth’s core, proposed by Braginsky and Meytlis (1990), and show that it is plausible for core parameters not only in polar regions but extends to mid- and low-latitudes where rotation and gravity are not parallel, except in a very thin equatorial layer. In this model the turbulence is highly anisotropic with preferred directions imposed by the Earth’s rotation and the magnetic field. Current geodynamo computations effectively model sub-grid scale turbulence by using isotropic viscous and thermal diffusion values significantly greater than the molecular values of the Earth’s core. We consider a local turbulent dynamo model for the Earth’s core in which the mean magnetic field, velocity and temperature satisfy the Boussinesq induction, momentum and heat equations with an isotropic turbulent Ekman number and Roberts number. The anisotropy is modelled only in the thermal diffusion tensor with the Earth’s rotation and magnetic field as preferred directions. Nonlocal organising effects of gravity and rotation (but not aspect ratio in the Earth’s core) such as an inverse cascade and nonlocal transport are assumed to occur at longer length scales, which computations may accurately capture with sufficient resolution. To investigate the implications of this anisotropy for the proposed turbulent dynamo model we investigate the linear instability of turbulent magnetoconvection on length scales longer than the background turbulence in a rotating sphere with electrically insulating exterior for no-slip and isothermal boundary conditions. The equations are linearised about an axisymmetric basic state with a conductive temperature, azimuthal magnetic field and differential rotation. The basic state temperature is a function of the anisotropy and the spherical radius. Elsasser numbers in the range 1–20 and turbulent Roberts numbers 0.01–1 are considered for both equatorial symmetries of the magnetic basic state. It is found that anisotropic turbulent thermal diffusivity has a strong destabilising effect on magneto-convective instabilities, which may relax the tight energy budget constraining geodynamo models. The enhanced instability is not due to a reduction of the total diffusivity. The anisotropy also strengthens instabilities which break the symmetry of the underlying state, which may facilitate magnetic field reversal. Geostrophic flow appears to suppress the symmetry breaking modes and magnetic instabilities. Through symmetry breaking and the geostrophic flow the anisotropy may provide a mechanism of magnetic field reversal and its suppression in computational dynamo models.

Influence of growth velocity variations on the pattern formation during the directional solidification of ternary eutectic Al-Ag-Cu

In order to control the evolving microstructure in complex eutectics and other multi-phase systems, it is important to understand the adjustment mechanisms and the parameters that determine pattern evolution. Here, a combined experimental and simulation approach is taken to investigate the response of a three-phase eutectic system to changes in solidification velocity. Using Al-Ag-Cu as a model system, large scale three-dimensional phase-field simulations are compared to directionally solidified samples containing both, velocity increases and decreases. The experimental results are obtained by synchrotron tomography for detailed consideration of the microstructure directly before and after a targeted velocity change and by traditional SEM analysis of sample cross sections to capture effects over longer length scales. In addition to qualitative analysis of the images, the microstructures are statistically assessed using phase fractions, shape factor and nearest neighbor statistics. Both, simulation and experiment show an immediate change in phase fraction as a result of a change in growth velocity. Adjustment of the microstructural pattern occurs more slowly over a relatively long length scale, due to splitting, merging and overgrowing events. Novel quantification techniques emphasize that ternary eutectic phase arrangements are complex and continuously evolving structures which, even under ideal conditions, do not reach steady state growth as quickly as previously believed.

The effect of reactions on the formation and readout of the gradient of Bicoid

During early development, the establishment of gradients of transcriptional factors determines the patterning of cell fates. The case of Bicoid (Bcd) in Drosophila melanogaster embryos is well documented and studied. There are still controversies as to whether SDD models in which Bcd is Synthesized at one end, then Diffuses and is Degraded can explain the gradient formation within the timescale observed experimentally. The Bcd gradient is observed in embryos that express a Bicoid-eGFP fusion protein (Bcd-GFP) which cannot differentiate if Bcd is freely diffusing or bound to immobile sites. In this work we analyze an SDID model that includes the Interaction of Bcd with binding sites. We simulate numerically the resulting full reaction–diffusion system in a cylindrical domain using previously determined biophysical parameters and a simplified version of the Bcd source. In this way we obtain solutions that depend on the spatial location approximately as observed experimentally and that reach such dependence at a time that is also compatible with the experimental observations. Analyzing the differences between the free and bound Bcd distributions we observe that the latter spans over a longer lengthscale. We conclude that deriving the lengthscale from the distribution of Bcd-GFP can lead to an overestimation of the gradient lengthscale and of the Hill coefficient that relates the concentrations of Bcd and of the protein, Hunchback, whose production is regulated by Bcd.

Magnetic stripes and holes: Complex domain patterns in perforated films with weak perpendicular anisotropy

Hexagonal antidot arrays have been patterned on weak perpendicular magnetic anisotropy NdCo films by e-beam lithography and lift off. Domain structure has been characterized by Magnetic Force Microscopy at remanence. On a local length scale, of the order of stripe pattern period, domain configuration is controlled by edge effects within the stripe pattern: stripe domains meet the hole boundary at either perpendicular or parallel orientation. On a longer length scale, in-plane magnetostatic effects dominate the system: clear superdomains are observed in the patterned film with average in-plane magnetization along the easy directions of the antidot array, correlated over several antidot array cells.

Stabilization of aqueous dispersions of poly(methacrylic acid)-coated iron oxide nanoparticles by double hydrophilic block polyelectrolyte poly(ethylene oxide)-block-poly(N-methyl-2-vinylpyridinium iodide)

Aqueous dispersions of poly(methacrylic acid)-coated superparamagnetic iron oxide nanoparticles (PMAA@SPIONs) and nanoparticles obtained by adding a layer of double-hydrophilic cationic block polyelectrolyte poly(ethylene oxide)-block-poly(N-methyl-2-vinylpyridinium iodide) (PEO-QP2VP) on PMAA@SPIONs were studied by a combination of static and dynamic light scattering, SAXS, transmission electron microscopy and atomic force microscopy, probing the structure of the SPION aggregates on the lengthscale from 1 to 103nm. Both SALS and AFM results indicate that adding a PEO-QP2VP layer to PMAA@SPIONs decreases the size of SPION aggregates formed in the dispersions. While TEM micrographs show that PEO-QP2VP@PMAA@SPION particles are less apt to form small clusters with the size of several tens nm compared to PMAA@SPION particles, the local clustering has no effect on the power law scattering behavior (I(q)∼q−1.4) of the SPION dispersions at longer lengthscales (tens to hundreds nm), which reflects mainly polydispersity of the aggregates.

Local and average structures of BaTiO3-Bi(Zn1/2Ti1/2)O3

The complex crystallographic structures of (1−x)BaTiO3-xBi(Zn1/2Ti1/2)O3 (BT-xBZT) are examined using high resolution synchrotron X-ray diffraction, neutron diffraction, and neutron pair distribution function (PDF) analyses. The short-range structures are characterized from the PDFs, and a combined analysis of the X-ray and neutron diffraction patterns is used to determine the long-range structures. The results demonstrate that the structure appears different when averaged over different length scales. In all compositions, the local structures determined from the PDFs show local tetragonal distortions (i.e., c/a > 1). However, a box-car fitting analysis of the PDFs reveals variations at different length scales. For 0.80BT-0.20BZT and 0.90BT-0.10BZT, the tetragonal distortions decrease at longer atom-atom distances (e.g., 30 Å vs. 5 Å). When the longest distances are evaluated (r > 40 Å), the lattice parameters approach cubic. Neutron and X-ray diffraction yield further information about the long-range structure. Compositions 0.80BT-0.20BZT and 0.90BT-0.10BZT appear cubic by Bragg diffraction (no peak splitting), consistent with the PDFs at long distances. However, these patterns cannot be adequately fit using a cubic lattice model; modeling their structures with the P4mm space group allows for a better fit to the patterns because the space group allows for c-axis atomic displacements that occur at the local scale. For the compositions 0.92BT-0.08BZT and 0.94BT-0.06BZT, strong tetragonal distortions are observed at the local scale and a less-distorted tetragonal structure is observed at longer length scales. In Rietveld refinements, the latter is modeled using a tetragonal phase. Since the peak overlap in these two-phase compositions limits the ability to model the local-scale structures as tetragonal, it is approximated in the refinements as a cubic phase. Collectively, the results demonstrate that alloying BT with BZT results in increased disorder and disrupts the long-range ferroelectric symmetry present in BT, while the large tetragonal distortion present in BZT persists at the local scale.

Microfibres and macroscopic films from the coordination-driven hierarchical self-assembly of cylindrical micelles.

Anisotropic nanoparticles prepared from block copolymers are of growing importance as building blocks for the creation of synthetic hierarchical materials. However, the assembly of these structural units is generally limited to the use of amphiphilic interactions. Here we report a simple, reversible coordination-driven hierarchical self-assembly strategy for the preparation of micron-scale fibres and macroscopic films based on monodisperse cylindrical block copolymer micelles. Coordination of Pd(0) metal centres to phosphine ligands immobilized within the soluble coronas of block copolymer micelles is found to induce intermicelle crosslinking, affording stable linear fibres comprised of micelle subunits in a staggered arrangement. The mean length of the fibres can be varied by altering the micelle concentration, reaction stoichiometry or aspect ratio of the micelle building blocks. Furthermore, the fibres aggregate on drying to form robust, self-supporting macroscopic micelle-based thin films with useful mechanical properties that are analogous to crosslinked polymer networks, but on a longer length scale.

Influence of long-scale length radial electric field components on zonal flow-like structures in the TJ-II stellarator

The influence of long-scale length radial electric fields on zonal flows-like structures has been studied in the TJ-II stellarator. This relation has been investigated in the edge plasma using two electrical rake probes. The results presented here show an empirical correlation between the properties of long-range correlations (LRCs) with zonal flow-like structures and the magnitude of radial (neoclassical, NC) electric fields in TJ-II neutral beam heated plasmas. These experimental findings show that the enhancement of the NC radial electric field increases the magnitude of LRCs, considered as a proxy of zonal flows, while the radial correlation length of the plasma potential fluctuations was found to decrease by about 40%. A strong relation between the magnitude of electric field structures with long and short radial scales was found. The calculated shearing rate corresponding to the short scale length structures of the radial electric field may be sufficient to regulate turbulence.