Anisotropic Orientation Distribution Research Articles

Molecular Structure Refinement Based on Residual Dipolar Couplings: A Comparison of the Molecular Rotational-Sampling Method with the Alignment-Tensor Approach.

In NMR experiments, residual dipolar couplings (RDCs) in a molecule can be measured by averaging the dipolar couplings (DCs) over the rotational motion of a molecule in an environment that induces a slight anisotropic orientation distribution of the molecule. Since the shape of the anisotropic distribution cannot be measured, it is standard practice to use a particular orientation distribution of the molecule with respect to the magnetic field, in the form of a so-called alignment tensor (AT), to calculate RDC-values for the molecule. Since the same alignment tensor is commonly used to calculate the different RDCs of a molecule, this approach rests on the assumption that the rotational motion of the molecule is decoupled from its internal motions and that the molecule is rigid. The validity of these two assumptions is investigated for a small, simple molecule, using a relatively rigid atomic interaction function or force field and a more flexible one. By simulating the molecule using an orientation-biasing force an anisotropic rotational distribution can be generated, for which RDCs can be obtained. Using these RDCs as target RDCs when applying one of the two approaches of structure refinement based on RDCs, it can be investigated how well the target RDCs are approximated in the RDC restraining and whether the corresponding nonuniform orientation distribution is reproduced. For the relatively rigid version of the molecule, the AT approach reproduces the target RDC-values, although the nonuniform orientation distribution of the angle θab,H between the vector r⃗ab connecting two atoms a and b in the molecule and the vector representing the direction of the magnetic field H⃗ as generated in the orientation-biasing simulation cannot be reproduced in the AT RDC-restraining simulation. For the relatively flexible version of the molecule, the AT approach fails to reproduce both the target RDC values and the nonuniform orientation distribution. For biomolecules with flexible parts, the application of the AT approach is thus not recommended. Instead, a method based on sampling of the rotational and internal degrees of freedom of the molecule should be applied in molecular structure determination or refinement based on measured RDCs.

Optimal alignment for maximizing the uniaxial modulus of 2D anisotropic random nanofiber networks

ABSTRACT Nanofiber networks are effective structural forms to utilize the excellent nanoscale properties of nanofibers in macro scale. Properly tuning the anisotropic degree of fiber orientation distribution can maximize the macroscopic mechanical properties of random nanofiber networks in a specific direction. However, the reinforcing mechanism of the anisotropic orientation distribution to the elastic behavior has not been fully understood. In this paper, the effect of anisotropic orientation distribution of nanofibers on the elastic behavior of network is studied based on the modulus-density scaling relation and stiffness thresholds. The uniaxial modulus of network is determined by both the orientation angle of each fiber and interconnectivity of the random fiber network. With the increase of anisotropic degree, the contribution of fiber orientation angle to the network modulus of the preferential direction increases and gradually tends to a constant, while the interconnectivity of the networks decreases, which may reduce the loadability of network. Therefore, at a given network density, the uniaxial modulus along the preferential direction first increases to a maximum value and then decreases with the increase of the anisotropic degree. Furthermore, an expression to predict the optimal anisotropic degrees corresponding to the maximum uniaxial moduli at different network densities is established.

Orientation anisotropies in macaque visual areas

In mammals, a larger number of neurons in V1 are devoted to cardinal (horizontal and vertical) orientations than to oblique orientations. However, electrophysiological results from the macaque monkey visual cortex are controversial. Both isotropic and anisotropic orientation distributions have been reported. It is also unclear whether different visual areas along the visual hierarchy have different orientation anisotropies. We analyzed orientation maps in a large set of intrinsic signal optical imaging data and found that both V1 and V4 exhibited significant orientation anisotropies. However, their overrepresented orientations were very different: in V1, both cardinal and radial orientations were overrepresented, while in V4, only cardinal bias was presented. These findings suggest that different cortical areas have evolved to emphasize different features that are suitable for their functional purposes, a factor that needs to be considered when efforts are made to explain the relationships between the visual environment and the cortical representation and between the cortical representation and visual perception.

Advances in NMR Spectroscopy of Weakly Aligned Biomolecular Systems.

The measurement and application of residual dipolar couplings (RDCs) in solution NMR studies of biological macromolecules has become well established over the past quarter of a century. Numerous methods for generating the requisite anisotropic orientational molecular distribution have been demonstrated, each with its specific strengths and weaknesses. In parallel, an enormous number of pulse schemes have been introduced to measure the many different types of RDCs, ranging from the most widely measured backbone amide 15N-1H RDCs, to 1H-1H RDCs and couplings between low-γ nuclei. Applications of RDCs range from structure validation and refinement to the determination of relative domain orientations, the measurement of backbone and domain motions, and de novo structure determination. Nevertheless, it appears that the power of the RDC methodology remains underutilized. This review aims to highlight the practical aspects of sample preparation and RDC measurement while describing some of the most straightforward applications that take advantage of the exceptionally precise information contained in such data. Some emphasis will be placed on more recent developments that enable the accurate measurement of RDCs in larger systems, which is key to the ongoing shift in focus of biological NMR spectroscopy from structure determination toward gaining improved understanding of how molecular flexibility drives protein function.

Importance of deformation-induced local orientation distributions for nucleation of recrystallisation

Nucleation in an aluminium tricrystal cold rolled along its columnar direction, to 40% thickness reduction, is studied. This experimental configuration was used to obtain the same deformation microstructure through the sample length, which made it possible to cut it into several slices of similar microstructures and use these slices differently. Some slices served to analyse the deformation microstructure and others to analyse the annealing microstructure. Nucleation developed only in one of the three crystals and not at grain boundaries. The relationship between the crystallographic orientations and the local density of nuclei and different attributes of the parent, deformation microstructure was then analysed. As generally presumed, the nuclei were observed to inherit orientations from the parent matrix. Much more surprisingly, the stored energy alone, which is often considered as the driving force for recrystallisation nucleation, was found not to provide a reliable criterion for recrystallisation nucleation in the investigated sample. Instead, the density of nuclei was the highest where the substructure is composed of sharp bands, which correspond to regions of highly anisotropic orientation distributions. A new energy criterion for recrystallisation nucleation is proposed, which is called “primary stored energy” and depends on the stored energy and the anisotropy of the orientation distribution.

Mean-field homogenization of thermoelastic material properties of a long fiber-reinforced thermoset and experimental investigation

Fiber-reinforced polymers contribute significantly to weight-reducing components for various industrial applications. A discontinuous glass fiber-reinforced thermoset resin is considered which is produced by the sheet molding compound (SMC) process. Related to the production process, the samples considered in this work exhibit an anisotropic fiber orientation distribution which highly affects the thermomechanical properties. The thermoviscoelastic material behavior of three selected samples is characterized by means of dynamic mechanical analysis. These tests show the temperature-dependent elastic modulus and the glass transition of the composite. Measurements of the thermal expansion of the SMC composite provide data on the coefficient of thermal expansion (CTE). These experimental investigations provide data for the thermoelastic material modeling. Aiming at the prediction of the effective thermal and mechanical properties, a Hashin–Shtrikman-based homogenization method is presented. Based on an eigenstrain formulation, the effective Young’s modulus and CTE are computed in two steps. Moreover, the mean-field method is given in dependence of a variable reference stiffness allowing to tailor the approach to the material system. The influence of this variable reference stiffness on the effective quantities as well as the predicted behavior is analyzed with respect to the experiments. The presented numerical results are in good agreement with the experimental data.

Sectional analysis for design of ultra-high performance fiber reinforced concrete beams with passive reinforcement

Sectional flexural analysis, as performed in normal strength concrete design, requires uniaxial constitutive models. For ultra-high performance fiber reinforced concrete (UHPFRC), the constitutive model tensile backbone varies with section heights for different flexural members, due to the size-dependent stress-crack opening relation used to derive it. In this paper, several simplified size-independent constitutive models were investigated. For unreinforced sections with heights between 51 mm and 1067 mm, the elastic-perfectly-plastic tension model leads to conservative ultimate moment prediction (or results within 5%) when compared to that obtained by the size-dependent model. For reinforced sections, the difference between the two models is affected by the reinforcing condition and is even smaller than the unreinforced cases. By assuming an elastic-perfectly-plastic tension model, the flexural strength of rectangular or T section UHPFRC beams was estimated analytically. The flexural strengths are greatly influenced by the reinforcement ratio and yielding strength of the longitudinal reinforcement. Including shear strength predictive equations from past research, the load capacity and failure mode for rectangular and T beams are presented in a design chart. The impact of several factors on UHPFRC beam flexural responses were investigated, such as different compressive strength, curing conditions, and anisotropic fiber orientation distributions. The load-deflection relationships generated from beam flexural analysis were compared to experimental results for both unreinforced and reinforced beams, with or without fiber alignment. Factors affecting the first crack strength in tension (i.e., fiber orientation distribution) had greater impact on the flexural strength of UHPFRC beams than the effect of using a size-dependent model.

Numerical predictions of fiber orientation and mechanical properties for injection‐molded long‐carbon‐fiber thermoplastic composites

The use of long carbon fiber‐reinforced thermoplastic composites as lightweight automotive materials offers superior mechanical performance compared to glass fibers. However, the anisotropic fiber orientation distribution with shell–core structure is critical to determine mechanical properties. Recently, both theoretical models of fiber orientation—Anisotropic Rotary Diffusion and Reduced Strain Closure and Improved Anisotropic Rotary Diffusion and Retarding Principal Rate—have been significantly developed in the field of fiber suspension rheology. From injection molding simulations, numerical predictions of fiber orientation are derived with related experimental validations, while dramatic changes in orientation distribution are discussed at various fiber concentrations and different polymer matrices. More importantly, the reinforcing ability is discussed in regard to the tensile modulus and the stress–strain response for a variety of long carbon fiber composites. POLYM. COMPOS., 39:3726–3739, 2018. © 2017 Society of Plastics Engineers

Magnetic field-induced effects on NMR properties

In principle, all the NMR observables, spin-spin coupling J, nuclear shielding σ and quadrupole coupling q, are magnetic field-dependent. The field dependence may be classified into two categories: direct and indirect (apparent) dependence. The former arises from the magnetic field-induced deformation of the molecular electronic cloud, while the latter stems from a slightly anisotropic orientation distribution of molecules, due to the interaction between the anisotropy of the molecular susceptibility tensor and the external magnetic field. Here we use 1,3,5-D3-benzene as a model system to investigate the indirect effect on the one-bond 1H-13C and 2H-13C spin-spin couplings (J couplings) and the 2H quadrupole coupling. Experiments carried out at four magnetic fields (4.7, 9.4, 14.1, and 18.8 T) show that the indirect effect is significant already at the magnetic fields commonly used in NMR spectrometers. A joint fit of the data extracted at the different field strengths provides experimental results for the susceptibility anisotropy, 2H quadrupole coupling constant and the related asymmetry parameter, as well as the one-bond CH and CD coupling constants extrapolated to vanishing field strength. The field-induced contributions are found to exceed the commonly assumed error margins of the latter. The data also indicate a primary isotope effect on the one-bond CH coupling constant. There is a tendency to further increase the magnetic field of NMR spectrometers, which leads to more pronounced indirect contributions and eventually significant direct effects as well.

Engineering Human TMJ Discs with Protein-Releasing 3D-Printed Scaffolds

The temporomandibular joint (TMJ) disc is a heterogeneous fibrocartilaginous tissue positioned between the mandibular condyle and glenoid fossa of the temporal bone, with important roles in TMJ functions. Tissue engineering TMJ discs has emerged as an alternative approach to overcoming limitations of current treatments for TMJ disorders. However, the anisotropic collagen orientation and inhomogeneous fibrocartilaginous matrix distribution present challenges in the tissue engineering of functional TMJ discs. Here, we developed 3-dimensional (3D)–printed anatomically correct scaffolds with region-variant microstrand alignment, mimicking anisotropic collagen alignment in the TMJ disc and corresponding mechanical properties. Connective tissue growth factor (CTGF) and transforming growth factor beta 3 (TGFβ3) were then delivered in the scaffolds by spatially embedding CTGF- or TGFβ3-encapsulated microspheres (µS) to reconstruct the regionally variant fibrocartilaginous matrix in the native TMJ disc. When cultured with human mesenchymal stem/progenitor cells (MSCs) for 6 wk, 3D-printed scaffolds with CTGF/TGFβ3-µS resulted in a heterogeneous fibrocartilaginous matrix with overall distribution of collagen-rich fibrous structure in the anterior/posterior (AP) bands and fibrocartilaginous matrix in the intermediate zone, reminiscent of the native TMJ disc. High dose of CTGF/TGFβ3-µS (100 mg µS/g of scaffold) showed significantly more collagen II and aggrecan in the intermediate zone than a low dose (50 mg µS/g of scaffold). Similarly, a high dose of CTGF/TGFβ3-µS yielded significantly higher collagen I expression in the AP bands compared with the low-dose and empty µS. From stress relaxation tests, the ratio of relaxation modulus to instantaneous modulus was significantly smaller with CTGF/TGFβ3-µS than empty µS. Similarly, a significantly higher coefficient of viscosity was achieved with the high dose of CTGF/TGFβ3-µS compared with the low-dose and empty µS, suggesting the dose effect of CTGF and TGFβ3 on fibrocartilage formation. Together, our findings may represent an efficient approach to engineering the TMJ disc graft with anisotropic scaffold microstructure, heterogeneous fibrocartilaginous matrix, and region-dependent viscoelastic properties.

Highly selective mixed-matrix membranes with layered fillers for molecular separation

Two-dimensional (2D) layered porous materials are of a considerable interest to researchers due to differences in the sizes of in-plane and out-of-plane confinement. These layered materials have been blended with polymers for the fabrication of mixed-matrix membranes (MMMs) for applications involving separation. The polymers in MMMs serve as a matrix and the 2D layered materials serve as filler used to enhance the separation performance (diffusivity and selectivity) of the polymeric matrix. Unfortunately, the existing models for estimating the effective diffusivity of MMMs with layered fillers are unable to provide reliable predictions. This study proposed a numerical approach to the estimation of effective diffusivity and the selectivity of MMMs using layered fillers based on the mass transfer simulations. In the proposed models, we took into account two critical parameters of the layered fillers: anisotropic diffusivity and orientation distributions. The predictive ability of the proposed approach was evaluated via comparison with experimental data. Finally, we outline the design of highly selective MMMs with layered porous materials based on the proposed methodology.

Polarization entanglement of sum-frequency photons: A tool to probe the Markovian limit

The article addresses the possibility of entanglement-specific infrared-visible sum-frequency generation spectroscopy. In the case of an anisotropic interface, it is possible to employ SSS and PSS polarizations to detect responses not only specific to ${\ensuremath{\chi}}_{YYY}$ and ${\ensuremath{\chi}}_{XYY}$ nonlinearities, but also to higher-order ${\ensuremath{\chi}}_{(YYY)(XYY)}$ and ${\ensuremath{\chi}}_{(XYY)(YYY)}$ nonlinearities. Using quantum mechanical studies of the rhenium complex $[\mathrm{Re}{(\mathrm{OH})}_{3}{(\mathrm{CO})}_{3}]$ as a molecular model, we demonstrate that if such complexes would form an anisotropic orientational distribution at a surface, under the considered geometry and the polarization settings, we may prepare quantum correlated $\mathrm{C}=\mathrm{O}$ vibrational states to emit polarization-entangled photons. Accordingly, we explore the possibility of a polarization-measurement protocol to extract spectral signatures of the entangled states. The response would be informative on intramolecular interactions. As a result, we discuss the possible practical implications in probing dynamics at interfaces, and different opportunities in the preparation of entangled vibrational states of quantified fidelity.

Strong anisotropic lifetime orientation distributions of a two-level quantum emitter around a plasmonic nanorod.

Spontaneous emission lifetime orientation distributions of a two-level quantum emitter in metallic nanorod structures are theoretically investigated by the rigorous electromagnetic Green function method. It was found that spontaneous emission lifetime strongly depended on the transition dipole orientation and the position of the emitter. The anisotropic factor defined as the ratio between the maximum and minimum values of the lifetimes along different dipole orientations can reach up to 103. It is much larger than those in dielectric structures which are only several times usually. Our results show that the localized plasmonic resonance effect provides a new degree of freedom to effectively control spontaneous emission by the dipole orientation of the quantum emitters.

Simulation of Cleavage Crack Propagation in Steels with Anisotropic Crystal Orientation Distribution

A model to simulate cleavage crack propagation in steels with anisotropic crystal orientation is proposed. The model is based on a criterion that one of the three {100} planes having highest normal stress exceeding the critical stress is selected as a cleavage plane in a grain in front of a crack tip. The normal stress on {100} planes is calculated from linear elastic crack tip stress field and crystal orientation distribution. The crack tip stress field is calculated from mixed mode stress intensity factors derived from first-order approximations where crack surface irregularity and crack front non-straightness, crack closing force acting at ridges between cleavage facets are considered. The crystal orientation distribution is obtained by Electron Back Scattering Diffraction (EBSD) measurement. Using the model, we simulated cleavage crack propagations for different specimen directions in a steel with texture. First, we compared simulated fracture surface morphology with the actual fracture surfaces obtained from small crack arrest test specimens. Both morphologies showed good agreement. Next, we simulated crack propagation at different crack orientations with the use of the model and examined a dependence of crack propagation resistance on crack orientation. Anisotropy of arrest crack length simulated by the model corresponded to that observed in the small crack arrest tests. Therefore, the model can simulate cleavage crack propagation considering anisotropic crystal orientation distribution.

Parametric and non-parametric statistical approaches to the determination of paleostress from dilatant fractures: Application to an Early Miocene dike swarm in central Japan

Several methods have been proposed for determining paleostress states from orientations of dilatant fractures such as dikes and veins. Recently a stochastic inversion method was invented to objectively estimate the principal stress axes and the stress ratio. Whether a fracture is dilated or not is controlled by the balance of the fluid pressure and the normal stress acting on it. The magnitude of normal stress depends on the fracture orientation, which causes anisotropic orientation distribution of dilatant fractures. The inversion method assumes that the orientation distribution of fractures can be approximated by a Bingham distribution, an exponential probability distribution on the unit sphere, of which symmetric axes are interpreted as the principal stress axes. However, it is unknown if the exponential type of distribution function is suitable or not. Here, we examine the distribution functions and propose two improved methods. One method uses the shifted power-law function as the shape of probability distribution, which is more flexible than the Bingham distribution and is applicable to various shapes of orientation distributions. Furthermore, an index of the driving fluid pressure can be estimated with a confidence interval. The other is a non-parametric (distribution-free) method, which can avoid the a priori assumption on the shape of distribution function without significantly losing accuracy or precision. The new methods were applied to an Early Miocene dike swarm formed during the back-arc opening of the Japan Sea. A normal-faulting stress regime with the minimum principal stress axis trending roughly perpendicular to the arc was obtained from the dikes. A moderately high stress ratio and a high fluid pressure were also estimated.

Influence of carding and drawing processes on orientation of fibers in slivers

The orientation of fibers is known to play a very important role in determining the quality of the carded and drawn slivers as well as the quality of the ultimate yarns produced from those slivers. Also, the orientation of fibers is considered to be a very useful parameter for evaluating the effectiveness of the carding and drawing processes in aligning the fibers. In addition, the orientation of fibers is known to determine the length utilization of the fibers in the slivers. This article reports on the influence of carding and drawing processes on the orientation of fibers in the carded and drawn slivers. A series of carded and drawn slivers were prepared by using polyester staple fibers and making various changes in the carding and drawing processes and the orientation of fibers in the slivers was evaluated based on Lindsley’s methodology in conjunction with a mathematical model of fiber orientation in slivers. It was observed that the increase in cylinder speed and the decrease in doffer speed resulted in more anisotropic fiber orientation distribution in the carded slivers and the degree of anisotropy was found to be more in the forward direction as compared to the backward direction of the carded slivers. The higher draft and doubling in the drawframe resulted in higher anisotropy in the orientation of fibers in the drawn slivers and the drawn slivers displayed more anisotropy in the backward direction as compared to the forward direction. The higher delivery speed of the drawframe resulted in higher anisotropy in fiber orientation in the drawn slivers and the drawn slivers exhibited more anisotropy in the backward direction as compared to the forward direction. The results of fiber orientation in the carded and drawn slivers obtained by using the mathematical model were compared to the fiber orientation parameters suggested by earlier researchers and a satisfactory correlation between them was observed.

Anisotropic Mechanical Behavior of Ni-base Alloy Weld Metal Considering Crystal Orientation Distribution

Microscopic stress distribution in cladded weld metal of Ni-base alloy was calculated. Simulation model of a columnar grain aggregate was generated based on a crystal orientation measurement result by electron backscatter diffraction method. Microscopic stress much higher than applied macroscopic stress was observed when load was applied along transverse direction of columnar grain growth direction. On the other hand, homogeneous microscopic stress was obtained in a columnar grain model when macroscopic stress was applied in columnar grain growth direction. The difference caused from anisotropic crystalline orientation distribution of weld metal, and is important in the evaluation of microscopic stress distribution in weld metal.

Incorporation in Langmuir and Langmuir–Blodgett films of symmetric fluorine substituted bent-core liquid crystals: Morphological and optical properties

Molecular mono- and multilayer films of a symmetric fluorine substituted bent-core liquid crystalline (LC) compound with hydrocarbon end-chains were prepared by the Langmuir and Langmuir–Blodgett (LB) technique. Langmuir films were characterized by surface pressure isotherms and Brewster angle microscopy. Likewise LB-films deposited onto amorphous glass substrates were characterized by ultraviolet–visible spectroscopy, the optical second harmonic generation technique and atomic force microscopy (AFM). Results show optimal non-centrosymmetric Z-type LB-film deposition for moderate number of layers ( n < 20); thereafter, an apparent collapse of the Z-type structure occurs, giving rise to a decrease of the nonlinear optical (NLO) properties. AFM, NLO and linear optical measurements suggest a uniform molecular coverage on the glass substrates and anisotropic orientational distribution; where, according to NLO-experimental data, the LC-bent-shaped molecules are preferably aligned toward the dipping direction with the net molecular polarization perpendicularly aligned to the substrate layer. This observation leads us to implement a simplified model based on the monomeric rod-like approximation, in order to estimate the significant NLO-tensor components.

A tensor approach to double wave vector diffusion-weighting experiments on restricted diffusion

Previously, it has been shown theoretically that in case of restricted diffusion, e.g. within isolated pores or cells, a measure of the pore size, the mean radius of gyration, can be estimated from double wave vector diffusion-weighting experiments. However, these results are based on the assumption of an isotropic orientation distribution of the pores or cells which hampers the applicability to samples with anisotropic or unknown orientation distributions, such as biological tissue. Here, the theoretical considerations are re-investigated and generalized in order to describe the signal dependency for arbitrary orientation distributions. The second-order Taylor expansion of the signal delivers a symmetric rank-2 tensor with six independent elements if the two wave vectors are concatenated to a single six-element vector. With this tensor approach the signal behavior for arbitrary wave vectors and orientation distributions can be described as is demonstrated by numerical simulations. The rotationally invariant trace of the tensor represents a pore size measure and can be determined from three orthogonal directions with parallel and antiparallel orientation of the two wave vectors. Thus, the presented tensor approach may help to improve the applicability of double wave vector diffusion-weighting experiments to determine pore or cell sizes, in particular in biological tissue.

Oriented Ensembles in Ultrafast Electron Diffraction

Electron scattering expressions are presented which are applicable to very general conditions of implementation of anisotropic ultrafast electron diffraction (UED) experiments on the femto- and picosecond time scale. "Magic angle" methods for extracting from the experimental diffraction patterns both the isotropic scalar contribution (population dynamics) and the angular (orientation-dependent) contribution are described. To achieve this result, the molecular scattering intensity is given as an expansion in terms of the moments of the transition-dipole distribution created by the linearly polarized excitation laser pulse. The isotropic component (n=0 moment) depends only on population and scalar internuclear separations, and the higher moments reflect bond angles and evolve in time due to rotational motion of the molecules. This clear analytical separation facilitates assessment of the role of experimental variables in determining the influence of anisotropic orientational distributions of the molecular ensembles on the measured diffraction patterns. Practical procedures to separate the isotropic and anisotropic components of experimental data are evaluated and demonstrated with application to reactions. The influence of vectorial properties (bond angles and rotational dynamics) on the anisotropic component adds a new dimension to UED, arising through the imposition of spatial order on otherwise randomly oriented ensembles.