Macroscopic Length Scales Research Articles

Modeling Nonequilibrium Gas Flow Based on Moment Equations

This article discusses the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium. Such a situation typically is present in rarefied or diluted gases, for flows in microscopic settings, or in general whenever the Knudsen number—the ratio between the mean free path of the particles and a macroscopic length scale—becomes significant. The continuum models are based on the stochastic description of the gas by Boltzmann's equation in kinetic gas theory. With moment approximations, extended fluid dynamic equations can be derived, such as the regularized 13-moment equations. Moment equations are introduced in detail, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low–Mach number setting for which both evolution equations and boundary conditions are well established. Conversely, nonlinear, high-speed processes require special closures that are still under development. Current approaches are examined, along with the challenge of computing shock wave profiles based on continuum equations.

High spatial resolution (1.1 μm and 20 nm) FTIR polarization contrast imaging reveals pre-rupture disorder in damaged tendon.

Collagen is a major constituent in many life forms; in mammals, collagen appears as a component of skin, bone, tendon and cartilage, where it performs critical functions. Vibrational spectroscopy methods are excellent for studying the structure and function of collagen-containing tissues, as they provide molecular insight into composition and organization. The latter is particularly important for collagenous materials, given that a key feature is their hierarchical, oriented structure, organized from molecular to macroscopic length scales. Here, we present the first results of high-resolution FTIR polarization contrast imaging, at 1.1 μm and 20 nm scales, on control and mechanically damaged tendon. The spectroscopic data are supported with parallel SEM and correlated AFM imaging. Our goal is to explore the changes induced in tendon after the application of damaging mechanical stress, and the consequences for the healing processes. The results and possibilities for the application of these high-spatial-resolution FTIR techniques in spectral pathology, and eventually in clinical applications, are discussed.

Mesoscopically ordered and 3D printed nanocomposites inspired from the ligament-bone interface

Event Abstract Back to Event Mesoscopically ordered and 3D printed nanocomposites inspired from the ligament-bone interface Anand Rajasekharan1, Romain Bordes1 and Martin Andersson1 1 Chalmers University of Technology, Chemistry and Chemical Engineering, Sweden Introduction: The insertion site between soft and hard tissues such as the bone-ligament interface is crucial for muscoskeletal function and is highly prone to injuries. The interface tissues have a complex variation in structure and chemical-biological composition[1]. Modern grafts that support such injured interfaces lack necessary mechanical fixation and regenerative capacity. An important factor required from synthetic grafts for such applications is to transfer and minimize stress concentrations at the insertion site. Natural interfaces achieve this with the help of a well-ordered structure and chemical heterogeneity[1]. In light of this, we have developed a mesoscopically ordered nanocomposite with a mineral gradient that might act as a graft plug at injured interfaces. The composite is inspired from the matrix heterogeneity of the ligament-bone interface in terms of mesostructural order, anisotropy and chemical composition. Methods: Inspired by the collagen organization in bone and ligament, we use lyotropic liquid crystalline (LC) gels possessing a mesoscopically ordered structure as the matrix[2]. To create a macroscopic, porous material, the plug was fabricated via traditional molds and 3D printing by combining two distinct LC inks (figure 1A and 1B). The LC combination was covalently photo-crosslinked to form resilient and flexible polymerized liquid crystal matrices (PLCs). Next, a compositional gradient of bone-like hydroxyapatite (HA) was formed in-situ within the aqueous domains of the part of the PLC possessing calcium and phosphate ions, yielding a 3D, composite material with a graded mineral content (figure 1A). Figure 1(A) A traditionally molded and (B) 3D printed, porous, heterogeneous nanocomposite with mineral gradient (C) SAXS scattering confirms presence of mesoscopic order and anisotropy in both the mineralized and non mineralized sections (D) SEM image shows differences in morphology between mineralized and non-mineralized sections of the composite (E) Elemental scan shows increasing calcium to carbon ratio along the length of the composite shown in figure 1D Results: Small angle X-ray scattering (SAXS) data of the nanocomposite confirms the presence of meso-ordered (hexagonal) structure with long-range anisotropy similar to bone (figure 1C). Moreover cross-sectional electron microscopy images of composites show a clear gradient of the HA nanoparticles along macroscopic length scales of the PLC matrix (figure 1D and 1E). We have also shown the possibility to fabricate these heterogeneous structures via 3D printing with a porous architecture, possibilities towards scaffolding a biological heterogeneity of cells. Current work focuses on studying the composites in-vitro with different cell lines to assess cell behaviour on the heterogeneous surfaces. Conclusion: In this work, we have developed a heterogeneous nanocomposite possessing a mesoscopically ordered structure and a controlled gradient in mineral density and mechanical stiffness, inspired by the well-ordered matrix heterogeneity observed in natural bone-ligament interfaces. Knut and Alice Wallenberg Foundation; MAX-lab (Lund, Sweden)

Analyzing Dirac Cone and Phonon Dispersion in Highly Oriented Nanocrystalline Graphene.

Chemical vapor deposition (CVD) is one of the most promising growth techniques to scale up the production of monolayer graphene. At present, there are intense efforts to control the orientation of graphene grains during CVD, motivated by the fact that there is a higher probability for oriented grains to achieve seamless merging, forming a large single crystal. However, it is still challenging to produce single-crystal graphene with no grain boundaries over macroscopic length scales, especially when the nucleation density of graphene nuclei is high. Nonetheless, nanocrystalline graphene with highly oriented grains may exhibit single-crystal-like properties. Herein, we investigate the spectroscopic signatures of graphene film containing highly oriented, nanosized grains (20-150 nm) using angle-resolved photoemission spectroscopy (ARPES) and high-resolution electron energy loss spectroscopy (HREELS). The robustness of the Dirac cone, as well as dispersion of its phonons, as a function of graphene's grain size and before and after film coalescence, was investigated. In view of the sensitivity of atomically thin graphene to atmospheric adsorbates and intercalants, ARPES and HREELS were also used to monitor the changes in spectroscopic signatures of the graphene film following exposure to the ambient atmosphere.

The Mechanobiology of Aging.

Aging is a complex, multifaceted process that induces a myriad of physiological changes over an extended period of time. Aging is accompanied by major biochemical and biomechanical changes at macroscopic and microscopic length scales that affect not only tissues and organs but also cells and subcellular organelles. These changes include transcriptional and epigenetic modifications; changes in energy production within mitochondria; and alterations in the overall mechanics of cells, their nuclei, and their surrounding extracellular matrix. In addition, aging influences the ability of cells to sense changes in extracellular-matrix compliance (mechanosensation) and to transduce these changes into biochemical signals (mechanotransduction). Moreover, following a complex positive-feedback loop, aging is accompanied by changes in the composition and structure of the extracellular matrix, resulting in changes in the mechanics of connective tissues in older individuals. Consequently, these progressive dysfunctions facilitate many human pathologies and deficits that are associated with aging, including cardiovascular, musculoskeletal, and neurodegenerative disorders and diseases. Here, we critically review recent work highlighting some of the primary biophysical changes occurring in cells and tissues that accompany the aging process.

From nanopores to macropores: Fractal morphology of graphite

We present a comprehensive structural characterization of two different highly pure nuclear graphites that compasses all relevant length scales from nanometers to sub-mm. This has been achieved by combining several experiments and neutron techniques: Small Angle Neutron Scattering (SANS), high-resolution Spin Echo SANS (SESANS) and neutron imaging. In this way it is possible to probe an extraordinary broad range of 6 orders of magnitude in length from microscopic to macroscopic length scales. The results reveal a fractal structure that extends from ∼0.6nm to 0.6 mm and has surface and mass fractal dimensions both very close to 2.5, a value found for percolating clusters and fractured ranked surfaces in 3D.

Ion Dynamics in Solid Electrolytes: NMR Reveals the Elementary Steps of Li+ Hopping in the Garnet Li6.5La3Zr1.75Mo0.25O12

Garnet-type oxides are considered to belong to the most attractive solid Li+ electrolytes. This is due to their wide electrochemical stability window as well as their superior ionic conductivity, with a Li-ion transference number of almost one. Usually ionic conductivities are studied via impedance spectroscopy on a macroscopic length scale. Time-domain NMR methods, however, have been used much less extensively to shed light on the elementary hopping processes in highly conducting oxide garnets. Here, we used NMR relaxometry and stimulated echo NMR to study Li+ self-diffusion in Li6.5La3Zr1.75Mo0.25O12 (LLZMO), which served as a model compound to collect information on the 7Li spin dynamics. It turned out that NMR spin–lattice relaxation (SLR) recorded in both the laboratory and rotating frame of reference shows features that seem to be a universal fingerprint for fast conducting garnets that have been stabilized in their cubic modification. In contrast to Al-doped garnet-type Li7La3Zr2O12 that modifies t...

The five-dimensional parameter space of grain boundaries

To specify a grain boundary at a macroscopic length scale requires the specification of five degrees of freedom. We use a specification in which three degrees of freedom associated with the boundary misorientation are in an orthogonal subspace from two associated with the mean boundary plane. By using Rodrigues vectors to describe rotations, we show how paths through these subspaces may be characterized. Some of these paths correspond to physical processes involving grain boundaries during microstructural evolution. Exploiting the orthogonality of the subspaces, a metric to measure ‘distance’ between two boundaries is defined in terms of the minimum set of rotations required to map one boundary on to the other. We compare our metric with others that have appeared. The existence of rotational symmetry in face-centred cubic crystals leads to as many as 2304 equivalent specifications of a boundary. We illustrate this multiplicity of descriptions for the (111) twin and a more general boundary. We present an algorithm to evaluate the geodesic distance between two boundaries, and apply it to identify the path along which the distance between these two boundaries is minimized. In general, the shortest path does not involve descriptions of boundary misorientations with the smallest misorientation angles.

Superconducting magnetoresistance in ferromagnet/superconductor/ferromagnet trilayers.

Magnetoresistance is a multifaceted effect reflecting the diverse transport mechanisms exhibited by different kinds of plain materials and hybrid nanostructures; among other, giant, colossal, and extraordinary magnetoresistance versions exist, with the notation indicative of the intensity. Here we report on the superconducting magnetoresistance observed in ferromagnet/superconductor/ferromagnet trilayers, namely Co/Nb/Co trilayers, subjected to a parallel external magnetic field equal to the coercive field. By manipulating the transverse stray dipolar fields that originate from the out-of-plane magnetic domains of the outer layers that develop at coercivity, we can suppress the supercurrent of the interlayer. We experimentally demonstrate a scaling of the magnetoresistance magnitude that we reproduce with a closed-form phenomenological formula that incorporates relevant macroscopic parameters and microscopic length scales of the superconducting and ferromagnetic structural units. The generic approach introduced here can be used to design novel cryogenic devices that completely switch the supercurrent ‘on’ and ‘off’, thus exhibiting the ultimate magnetoresistance magnitude 100% on a regular basis.

Magnetic order-disorder phase transition in Cr70Fe30 thin films

Dynamic magnetic response of Cr70Fe30 thin films with thickness in the range 11 nm ≤ t ≤ 978 nm and composition above the critical concentration for ferromagnetism was determined by measuring linear (χ1) and nonlinear (χ2 – χ5) ac-magnetic susceptibilities over three decades of frequency (101 – 104 Hz) in the temperature range 2–300 K. An elaborate analysis of χ1(T), measured in the absence or presence of a superposed dc magnetic field, Hdc, reveals that the asymptotic critical behavior of the films with t ≥ 21 nm is that of a three-dimensional (3D) isotropic dipolar ferromagnet. Interplay between long-range dipole–dipole and short-range exchange interactions causes a crossover to the 3D isotropic Heisenberg critical behavior when the temperature is increased above the Curie temperature, TC, outside the asymptotic critical region (ACR). By contrast, in the ACR, the film with t = 11 nm behaves as a 3D Ising ferromagnet. TC decreases with film thickness in accordance with the finite-size scaling with the value for the spin–spin correlation length exponent that corresponds to the 3D isotropic dipolar universality class. In the films with t ≤ 42 nm, besides the macroscopic length scale of the ferromagnetic order in the static limit, there exists a length scale that corresponds to finite spin clusters, whose dynamics is spin glass-like.

Additive manufacturing of mechanochromic polycaprolactone on entry-level systems

Purpose– This paper aims to explore and demonstrate the ability to integrate entry-level additive manufacturing (AM) techniques with responsive polymers capable of mechanical to chemical energy transduction. This integration signifies the merger of AM and smart materials.Design/methodology/approach– Custom filaments were synthesized comprising covalently incorporated spiropyran moieties. The mechanical activation and chemical response of the spiropyran-containing filaments were demonstrated in materials that were produced via fused filament fabrication techniques.Findings– Custom filaments were successfully produced and printed with complete preservation of the mechanochemical reactivity of the spiropyran units. These smart materials were demonstrated in two key constructs: a center-cracked test specimen and a mechanochromic force sensor. The mechanochromic nature of the filament enables (semi)quantitative assessment of peak loads based on color change, without requiring any external analytical techniques.Originality/value– This paper describes the first examples of three-dimensional-printed mechanophores, which may be of significant interest to the AM community. The ability to control the chemical response to external mechanical forces, in combination with AM to process the bulk materials, potentiates customizability at the molecular and macroscopic length scales.

Length scale dependent deformation in natural rubber

ABSTRACTStrong length scale dependent deformation has been previously observed in the elastomer polydimethylsiloxane by indentation type experiments at micro‐ to nanometer length scales with a sharp conical tip. To examine if other nonsilicone based elastomers exhibit similar length scale dependent deformation behavior, natural rubber has been chosen in this study. Performing indentation type tests with a nanoindentation system, the universal hardness and the elastic modulus are determined at different probing depths ranging from about 90 to 5 μm to characterize length scale dependent deformation behavior in natural rubber. The testing with a Berkovich tip resulted in an amazing increase in the universal hardness with decreasing probing depth indicating that the deformation mechanisms at the micrometer length scales are significantly different as compared to those at the macroscopic length scales. The observed length scale dependent deformation is associated with an increase in rotation gradients with decreasing probing depth. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 42683.

Film-Stabilizing Attributes of Polymeric Core-Shell Nanoparticles.

Self-organization of nanoparticles into stable, molecularly thin films provides an insightful paradigm for manipulating the manner in which materials interact at nanoscale dimensions to generate unique material assemblies at macroscopic length scales. While prior studies in this vein have focused largely on examining the performance of inorganic or organic/inorganic hybrid nanoparticles (NPs), the present work examines the stabilizing attributes of fully organic core-shell microgel (CSMG) NPs composed of a cross-linked poly(ethylene glycol dimethacrylate) (PEGDMA) core and a shell of densely grafted, but relatively short-chain, polystyrene (PS) arms. Although PS homopolymer thin films measuring from a few to many nanometers in thickness, depending on the molecular weight, typically dewet rapidly from silica supports at elevated temperatures, spin-coated CSMG NP films measuring as thin as 10 nm remain stable under identical conditions for at least 72 h. Through the use of self-assembled monolayers (SAMs) to alter the surface of a flat silica-based support, we demonstrate that such stabilization is not attributable to hydrogen bonding between the acrylic core and silica. We also document that thin NP films consisting of three or less layers (10 nm) and deposited onto SAMs can be fully dissolved even after extensive thermal treatment, whereas slightly thicker films (40 nm) on Si wafer become only partially soluble during solvent rinsing with and without sonication. Taken together, these observations indicate that the present CSMG NP films are stabilized primarily by multidirectional penetration of relatively short, unentangled NP arms caused by NP layering, rather than by chain entanglement as in linear homopolymer thin films. This nanoscale "velcro"-like mechanism permits such NP films, unlike their homopolymer counterparts of comparable chain length and thickness, to remain intact as stable, free-floating sheets on water, and thus provides a viable alternative to ultrathin organic coating strategies.

Evidence on the macroscopic length scale spin coherence for the edge currents in a narrow HgTe quantum well

We experimentally investigate spin-polarized electron transport between two ferromagnetic contacts, placed at the edge of a two-dimensional electron system with band inversion. The system is realized in a narrow (8~nm) HgTe quantum well, the ferromagnetic side contacts are formed from a pre-magnetized permalloy film. In zero magnetic field, we find a significant edge current contribution to the transport between two ferromagnetic contacts. We experimentally demonstrate that this transport is sensitive to the mutual orientation of the magnetization directions of two 200~$\mu$m-spaced ferromagnetic leads. This is a direct experimental evidence on the spin-coherent edge transport over the macroscopic distances. Thus, the spin is extremely robust at the edge of a two-dimensional electron system with band inversion, confirming the helical spin-resolved nature of edge currents.

64 A novel role for astrocytes in regulating glutamate clearance during stroke

We are building tools to confront a fundamental challenge of the brain and other complex biological systems: their molecular building blocks are nanoscale in size and organized with nanoscale precision, but support physiological processes and computations that occur over macroscopic length scales. To enable the understanding and fixing of such complex systems, we are creating tools that enable molecular-resolution maps of large scale systems, as well as technologies for observing and controlling information processing in such systems. First, we have developed a method for super-resolution optical imaging that can image large 3-D preserved specimens, with nanoscale precision (Chen et al., 2015). We embed a specimen in a swellable polymer, which upon exposure to water expands isotropically in size, enabling conventional diffraction-limited microscopes to do large-volume nanoscopy. Second, we have collaboratively developed plenoptic or light-field microscopy approaches to image fast physiological processes in 3-D with millisecond precision, and used them to image all the neural activity in small organisms (Prevedel et al., 2014). Third, we have collaboratively developed robotic and microfabricated methods for electrically recording the electrical activity of large numbers of cells in the brain (Kodandaramaiah et al., 2012). Finally, we have developed a set of genetically-encoded reagents known as optogenetic tools, that when expressed in specific neurons, enable their electrical activities to be precisely driven or silenced in response to millisecond timescale pulses of light (Boyden, 2011; Chuong et al., 2014; Klapoetke et al., 2014). In this way we aim to enable the systematic mapping, dynamical observation, and control of complex systems like the brain. References Boyden, E. S. (2011). A history of optogenetics: the development of tools for controlling brain circuits with light. F1000 Biology Reports 3(11). Chen, F., Tillberg, P. W., & Boyden, E. S. (2015). Expansion microscopy. Science 347, 543–548. Chuong, A. S., Miri, M. L., Busskamp, V., Matthews, G. A. C., Acker, L. C., Sorensen, A. T., ... Boyden, E. S. (2014) Noninvasive optical inhibition with a red-shifted microbial rhodopsin, Nature Neuroscience 17, 1123–1129. Klapoetke, N. C., Murata, Y., Kim, S. S., Pulver, S. R., Birdsey-Benson, A., Cho, Y. K., ... Boyden, E. S. (2014). Independent optical excitation of distinct neural populations. Nature Methods, 11, 338–346. Kodandaramaiah, S., Talei Franzesi, G., Chow, B., Boyden, E. S., & Forest, C. (2012). Automated whole-cell patch clamp electrophysiology of neurons in vivo. Nature Methods, 9, 585–587. Prevedel, R., Yoon, Y.-G., Hoffman, M., Pak, N., Wetzstein, G., Kato, S., ... Vaziri, A. (2014). Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy. Nature Methods, 11, 727–730.

Surface effects in nanoscale structures investigated by a fully-nonlocal energy-based quasicontinuum method

Surface effects in nanoscale mechanical systems such as nanoporous solids or small-scale structures can have a significant impact on the effective material response which deviates from the material behavior of bulk solids. Understanding such phenomena requires modeling techniques that locally retain atomistic information while transitioning to the relevant macroscopic length scales. We recently introduced a fully-nonlocal energy based quasicontinuum (QC) method equipped with new summation rules. This technique accurately bridges across scales from atomistics to the continuum through a thermodynamically-consistent coarse-graining scheme. Beyond minimizing energy approximation errors and spurious force artifacts, the new method also qualifies to describe free surfaces, which is reported here. Surfaces present a major challenge to coarse-grained atomistics, which has oftentimes been circumvented by costly ad hoc extensions of the traditional QC method. We show that our new coarse-graining scheme successfully and automatically reduces spurious force artifacts near free surfaces. After discussing the computational model, we demonstrate its benefits in the presence of free surfaces by several nanomechanical examples including surface energy calculations, elastic size effects in nano-rods and in plates with nano-sized holes. Overall, we demonstrate the importance of surface effects as well as a new strategy to accurately capture those computationally via coarse-grained atomistics.

Bone as a Structural Material.

As one of the most important natural materials, cortical bone is a composite material comprising assemblies of tropocollagen molecules and nanoscale hydroxyapatite mineral crystals, forming an extremely tough, yet lightweight, adaptive and multi-functional material. Bone has evolved to provide structural support to organisms, and therefore its mechanical properties are vital physiologically. Like many mineralized tissues, bone can resist deformation and fracture from the nature of its hierarchical structure, which spans molecular to macroscopic length-scales. In fact, bone derives its fracture resistance with a multitude of deformation and toughening mechanisms that are active at most of these dimensions. It is shown that bone's strength and ductility originate primarily at the scale of the nano to submicrometer structure of its mineralized collagen fibrils and fibers, whereas bone toughness is additionally generated at much larger, micro- to near-millimeter, scales from crack-tip shielding associated with interactions between the crack path and the microstructure. It is further shown how the effectiveness with which bone's structural features can resist fracture at small to large length-scales can become degraded by biological factors such as aging and disease, which affect such features as the collagen cross-linking environment, the homogeneity of mineralization, and the density of the osteonal structures.

A new cluster-type statistical model for the prediction of deformation textures

An attempt was done to improve the quality of deformation texture predictions by statistical models through the introduction of "clusters" of N grains thus defining a third, intermediate length scale. The interaction between each cluster and the macroscopic length scale is of the Taylor type, whereas inside each cluster a VPSC scheme is used. Predictions of cold rolling deformation textures were quantitatively compared with experimental results for a steel alloy. The results are encouraging.

Genetically improved monolayer-forming tobacco mosaic viruses to generate nanostructured semiconducting bio/inorganic hybrids.

The genetically determined design of structured functional bio/inorganic materials was investigated by applying a convective assembly approach. Wildtype tobacco mosaic virus (wt TMV) as well as several TMV mutants were organized on substrates over macroscopic-length scales. Depending on the virus type, the self-organization behavior showed pronounced differences in the surface arrangement under the same convective assembly conditions. Additionally, under varying assembly parameters, the virus particles generated structures encompassing morphologies emerging from single micrometer long fibers aligned parallel to the triple-contact line through disordered but dense films to smooth and uniform monolayers. Monolayers with diverse packing densities were used as templates to form TMV/ZnO hybrid materials. The semiconducting properties can be directly designed and tuned by the variation of the template architecture which are reflected in the transistor performance.

Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner

This paper applies topology optimisation to the design of structures with periodic and layered microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all microstructural details, as compared to the often used homogenisation approach. The approach takes boundary conditions into account and ensures connected and macroscopically optimised microstructures regardless of the difference in micro- and macroscopic length scales. This results in microstructures tailored for specific applications rather than specific properties. Manufacturability is further ensured by the use of robust topology optimisation. Dealing with the complete macroscopic structure and its response is computationally challenging as very fine discretisations are needed in order to resolve all microstructural details. Therefore, this paper shows the benefits of applying a contrast-independent spectral preconditioner based on the multiscale finite element method (MsFEM) to large structures with fully-resolved microstructural details. It is shown that a single preconditioner can be reused for many design iterations and used for several design realisations, in turn leading to massive savings in computational cost. The density-based topology optimisation approach combined with a Heaviside projection filter and a stochastic robust formulation is used on various problems, with both periodic and layered microstructures. The presented approach is shown to allow for the topology optimisation of very large problems in Matlab, specifically a problem with 26 million displacement degrees of freedom in 26 hours using a single computational thread.