Orientation Averaging Research Articles

Theory of electrical conductivity and dielectric permittivity of highly aligned graphene-based nanocomposites

Highly aligned graphene-based nanocomposites are of great interest due to their excellent electrical properties along the aligned direction. Graphene fillers in these composites are not necessarily perfectly aligned, but their orientations are highly confined to a certain angle, with 90° giving rise to the randomly oriented state and 0° to the perfectly aligned one. Recent experiments have shown that electrical conductivity and dielectric permittivity of highly aligned graphene-polymer nanocomposites are strongly dependent on this distribution angle, but at present no theory seems to exist to address this issue. In this work we present a new effective-medium theory that is derived from the underlying physical process including the effects of graphene orientation, filler loading, aspect ratio, percolation threshold, interfacial tunneling, and Maxwell–Wagner–Sillars polarization, to determine these two properties. The theory is formulated in the context of preferred orientational average. We highlight this new theory with an application to rGO/epoxy nanocomposites, and demonstrate that the calculated in-plane and out-of-plane conductivity and permittivity are in agreement with the experimental data as the range of graphene orientations changes from the randomly oriented to the highly aligned state. We also show that the percolation thresholds of highly aligned graphene nanocomposites are in general different along the planar and the normal directions, but they converge into a single one when the statistical distribution of graphene fillers is spherically symmetric.

Stiffness Prediction of Beech Wood Flour Polypropylene Composite by using Proper Fiber Orientation Distribution Function

One of the most famous methods to predict the stiffness of short fiber composites is micromechanical modeling. In this study, a Representative Volume Element (RVE) of a beech wood flour natural composite has been designed and the orientation averaging approach has been utilized to predict its stiffness tensor. The novelty of this work is in finding the proper fiber orientation distribution function to increase the precision of the stiffness prediction of this kind of natural composites. The predicted results for stiffness with the micromechanical modeling are compared to the experimental test results and FEM results of beech wood flour/polypropylene composite.

Can a periodic boundary model reproduce the longer-range density fluctuations in a real amorphous material?

Whereas the conventional definition of the static structure factor, S(Q), means that, for any sample or structural model, its value at zero Q, S(0), is identically equal to zero, the structures of ideally-disordered materials, such as single-phase liquids and amorphous solids, incorporate long-range density fluctuations that are characterised by a non-zero limiting value (S0) of S(Q≠0) as Q→0. An analysis of these density fluctuations in terms of their Fourier components leads to the definition of an ideally-disordered material as one that exhibits a continuous, isotropic distribution of Fourier wavelengths, A(Λ), that decays asymptotically to zero at Λ=∞. On the other hand, a similar analysis for a periodic boundary model reveals that the form of the intermediate-range order at higher inter-atomic distances, r, and that of the long-range density fluctuations are fundamentally different from those of a real amorphous material. The severely limited number of (especially the longer) allowed Fourier wavelengths, Λ, coupled with their strictly defined orientations within the unit cell of a periodic boundary model, means that such a model is inherently crystalline, and that no amount of orientational (polycrystalline) averaging can overcome this problem. The various methods of deriving S(Q) for both periodic-boundary and cluster models are discussed, and it is shown that, since a periodic boundary model is not ideally-disordered, a polycrystalline average does not yield a consistent value for S0, but one that is dependent on its exact method of calculation. It is therefore concluded that, to investigate the longer-range density fluctuations in amorphous materials, it is essential to employ a cluster model, rather than one generated with a periodic boundary.

Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM.

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol-1. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes.

Flow-induced anisotropic viscosity in short FRPs

BackgroundThe commonly used flow models for Fiber Reinforced Polymers (FRPs) often neglect the flow-induced anisotropy of the suspension, but with increasing fiber volume fraction, this plays an important role. There exist already some models which count on this effect. They are, however, phenomenological and need a fitted model parameter. In this paper, a micromechanically-based constitutive law is proposed which considers the flow-induced anisotropic viscosity of the fiber suspension.MethodsThe introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber suspension which depends on the actual fiber orientation distribution. Assuming incompressible material behaviour, a homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described based on Jeffery’s equation. The reorientation of the fibers is modeled in two ways: by describing them with fiber orientation vectors, and by fiber orientation tensors. A numerical implementation of the introduced model is applied to representative flow modes.ResultsThe predicted effective stress values depending on the actual fiber orientation distribution through the anisotropic viscosity are analyzed in transient and stationary flow cases. In the case of the assumed incompressibility, they show similar effective viscous material behaviour as the results obtained by the use of the Dinh-Armstrong constitutive law.ConclusionsThe introduced model is a possible way to describe the flow-induced anisotropic viscosity of a fluid-fiber suspension based on the mean field theory.

Homogenization and Materials Design of Anisotropic Multiphase Linear Elastic Materials Using Central Model Functions

It is shown in the present work that for linear elastic multiphase materials the orientation average of a stiffness tensor can be given in a closed form if central model functions are taken into consideration for the description of the material orientation distribution. This holds for arbitrary numbers of material constituents and for arbitrary degree of anisotropy of any of the constituents. The first-order bounds of Voigt and Reuss, the geometric average of Aleksandrov and Aisenberg and, specifically, the Hashin–Shtrikman bounds are given in closed forms depending on the single crystal stiffnesses of the material constituents, on their volume fractions and, for elasticity, on a central orientation and two scalar parameters per central model function. The central orientation and the two scalar parameters, referred to as texture eigenvalues in the present work, reflect the complete influence of the corresponding central model function on the elastic properties. The set of all admissible texture eigenvalues is derived. The closed form expressions can be used, e.g., for efficient and low dimensional homogenization procedures taking the crystallographic texture into account or, e.g., for the determination of estimates for unknown single crystal behavior. It is further shown, that central crystallite orientation distributions exist which conserve the anisotropy of the single crystal behavior but invert the direction of the anisotropy. The closed form expressions documented in the present work are used for an exemplary materials design problem in order to determine favorable volume fractions and texture eigenvalues for the orientation distributions of considered constituents for given prescribed anisotropic properties.

Flow‐induced anisotropic viscosity in short fiber reinforced polymers

AbstractThe commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid‐fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh‐Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth‐order fiber orientation tensor. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Juxta-terminal Helix Unwinding as a Stabilizing Factor to Modulate the Dynamics of Transmembrane Helices.

Transmembrane helices of integral membrane proteins often are flanked by interfacial aromatic residues that can serve as anchors to aid the stabilization of a tilted transmembrane orientation. Yet, physical factors that govern the orientation or dynamic averaging of individual transmembrane helices are not well understood and have not been adequately explained. Using solid-state (2) H NMR spectroscopy to examine lipid bilayer-incorporated model peptides of the GWALP23 (acetyl-GGALW(LA)6 LWLAGA-amide) family, we observed substantial unwinding at the terminals of several tilted helices spanning the membranes of DLPC, DMPC, or DOPC lipid bilayers. The fraying of helix ends might be vital for defining the dynamics and orientations of transmembrane helices in lipid bilayer membranes.

Inefficiency of orientation averaging: Evidence for hybrid serial/parallel temporal integration.

Intuition suggests that increased viewing time should allow for the accumulation of more visual information, but scant support for this idea has been found in studies of voluntary averaging, where observers are asked to make decisions based on perceived average size. In this paper we examine the dynamics of information accrual in an orientation-averaging task. With orientation (unlike intensive dimensions such as size), it is relatively safe to use an item's physical value as an approximation for its average perceived value. We displayed arrays containing eight iso-eccentric Gabor patterns, and asked six trained psychophysical observers to compare their average orientation with that of probe stimuli that were visible before, during, or only after the presentation of the Gabor array. From the relationship between orientation variance and human performance, we obtained estimates of effective set size, i.e., the number of items that an ideal observer would need to assess in order to estimate average orientation as well as our human observers did. We found that display duration had only a modest influence on effective set size. It rose from an average of ∼2 for 0.1-s displays to an average of ∼3 for 3.3-s displays. These results suggest that the visual computation is neither purely serial nor purely parallel. Computations of this nature can be made with a hybrid process that takes a series of subsamples of a few elements at a time.

Materials design of elastic properties of multiphase polycrystalline composites using model functions

AbstractFor a chosen combination of materials for a multiphase polycrystalline composite, a crystallite orientation distribution function for each phase is formulated as a superposition of analytic central model von Mises‐Fisher functions. The chosen central model functions allow the analytic integration of orientation averages of arbitrarily anisotropic fourth‐order tensors. Based on this result, the first‐order bounds of Voigt and Reuss and the geometric average of the stiffness can be expressed explicitly in closed forms for arbitrarily anisotropic polycrystalline materials and number of phases depending on the volume fractions and the influence of the crystallographic texture of each constituent. These expressions can then be used for the materials design aiming the determination of volume fractions and orientation distribution of selected materials for prescribed effective properties. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Goals Orientation and Pre Competitive Stress of Brasilians Track and Field Athletes

The aim of this study is correlate the level of the stress pre competitive with the motivational orientation of the young athletes who participate in the sport competition. Through a research correlational we studied 25 younger Brazilians athletes of athletics (mean age 15.20±1.91) in Santana de Parnaiba, Sao Paulo City, Brazil; as instrumental we applied the List Of Symptoms Of Stress Pre-Competitive Youth Children and Teosq, then we tested the stability of the instruments and their correlation. Corresponding to the Teosq scale the Alpha was 0.69 for ego orientations and 0.75 for task orientation; for the stress scale, the Alpha result was 0.86, the average of task orientation was 4.20 and ego orientation was 2.64 showing that the group has tendency to task orientation; the level of stress was moderate and no significant correlations was found. We can conclude that both instruments tested in this study had a stable reliability and the pre-competitive stress, can cause changes in the behavior of a consistent athlete before the competition, disfiguring your sleep, and during sports practice, impair its performance.

Estimation of the elastic constants of highly porous cellular plastics reinforced with fibres embedded in foam struts

In order to enhance the mechanical properties of polymer foams, fillers of different materials and sizes are being applied. Fibrous fillers shorter than the characteristic foam cell dimensions have the potential of efficient reinforcement, due to their high aspect ratio, without detrimentally interfering with foam structure. A theoretical model is developed for evaluation of the effect of filler on foam stiffness. The elastic response of rigid polymer foams filled with short fibres, of length commensurable with that of foam struts, is modelled by using the orientational averaging technique. Explicit expressions for components of the stiffness tensor of composite foams are derived in terms of elasticity characteristics of the polymer and reinforcing fibres, fibre content, foam density, and parameters of the orientational distribution of foam struts. The model is applied to describing the foam stiffness as a function of fibre loading of polyurethane foams filled with milled carbon fibres.

Quantification of voxel-wise total fibre density: Investigating the problems associated with track-count mapping

A biological parameter that would be valuable to be able to extract from diffusion MRI data is the local white matter axonal density. Track-density imaging (TDI) has been used as if it could provide such a measure; however, this has been the subject of controversy, primarily due to the fact that track-count quantitation is highly sensitive to tracking biases and errors. The spherical-deconvolution informed filtering of tractograms (SIFT) post-processing method was recently introduced to minimise tractography biases, and thus provides a more biologically meaningful measure that could be used in track-count mapping (i.e. TDI following SIFT). The TDI intensity following SIFT ideally corresponds to the orientational average of the fibre orientation distribution (FOD), which corresponds to the total Apparent Fibre Density (AFDtotal) within the AFD framework; in fact, AFDtotal provides a direct measure of local fibre density at native resolution that does not rely on fibre-tracking. In this study, we demonstrate problems associated with quantitative TDI investigations, which can be avoided by using SIFT processing or directly by using AFDtotal maps. We also characterise the intra- and inter-subject reproducibility of TDI maps (with and without SIFT pre-processing) and AFDtotal maps. It is shown that SIFT improves the quantitative characteristics of TDI, but is still vastly inferior to the properties of the AFDtotal parameter itself, because the latter does not require tracking. While standard TDI might be preferable in applications when high anatomical contrast is required, particularly when combined with super-resolution, for voxel-wise quantitation of total tract density (i.e. without tract orientation information) at native resolution, the total AFD maps are preferable to TDI or other related track-count maps. Regardless of the track-count measure, it should be noted that all of these voxel-averaged approaches discard important information that is retained in fibre-specific approaches such as AFD.

Structure factor of a Gaussian chain confined between two parallel plates.

We study the structure factor of a single Gaussian chain confined between two macroscopic parallel plates theoretically. The chain propagator is constructed in terms of the eigen-spectrum of the Laplace operator under the Dirichlet boundary condition enforced at the two plates, by which the confinement effect enters the treatment through size-dependent eigen-spectrum. In terms of the series expansion solution for the chain propagator, we first calculate the confinement free energy and the confinement force for an arbitrary confinement strength. It is found that the confinement force scales to the distance between the two confining surfaces with a power of -3 for strong confinements and of -2 for weak confinements. Based on the ground state dominance approximation for strong confinements and the Euler-Maclaurin formula for weak confinements, we develop approximation theories for the two limit situations, which agree with the numerical results well. We further calculate the structure factor of the confined Gaussian chain in this slit geometry. While the scattering function of the transverse chain fluctuations perpendicular to the confinement direction is still a Debye function form, the structure factor for the longitudinal fluctuations along the confinement dimension starts with the monotonic Debye function behavior for weak confinements and develops a decaying oscillation behavior with the increase of confinements. The numerical results for the structure factor are also interpreted by developing approximation theories in different confinement regimes. Finally, the orientational average of the anisotropic structure factor is performed and an analytic expression for the averaged structure factor is derived under the ground state dominance approximation for strong confinements.

Modeling of constitutive behavior of anisotropic composite material using multi-scale approach

The paper is focused on determining the elastic-plastic behavior of anisotropic composite materials. One of the main goals of this study is to compute effective material properties by analyzing material behavior at microstructure level. The effective material properties were investigated with the use of homogenization procedure connected with volume averaging of stress and strain values in RVE (Representative Volume Element). Three dimensional RVE geometry that represents material microstructure is taken into consideration. The spatial distribution of the particles is determined with experimental data. A boundary value problem is solved by using the finite element method and enforcing periodic boundary conditions. In addition, another approaches based on two step homogenization method and orientation averaging procedure are proposed. Results obtained numerically by using different approaches are presented, compared and related to the experimental results.DOI: http://dx.doi.org/10.5755/j01.mech.21.2.10276

On the dynamics of photo-electrons in C60

We explore photo-electron spectra (PES) and photo-electron angular distributions (PAD) of C60 with time-dependent density functional theory (TDDFT) in real time. To simulate experiments in gas phase, we consider isotropic ensembles of cluster orientations and perform orientation averaging of the TDDFT calculations. First, we investigate ionization properties of C60 by one-photon processes in the range of VUV energies. The PES map the energies of the occupied single-particle states, while the weights of the peaks in PES are given by the depletion of the corresponding level. The different influences can be disentangled by looking at PES from slightly different photon frequencies. PAD in the one-photon regime can be characterized by one parameter, the anisotropy. This single parameter unfolds worthwhile information when investigating the frequency and state dependences. We also discuss the case of multi-photon ionization induced by strong infrared laser pulses in C60. In agreement with measurements, we find that the PES show a regular comb of peaks separated by the photon energy. Our calculations reveal that this happens because only very few occupied states of C60 near the ionization threshold contribute to emission and that these few states happen to cooperate filling the same peaks. The PAD show a steady increase of anisotropy with increasing photon order.

Analytical homogenization of linear elasticity based on the interface orientation distribution – A complement to the self-consistent approach

We combine a laminate-based approach and an interface orientation average. For linear elasticity, we obtain analytical expressions for the effective stiffness of mixtures of two isotropic phases with isotropic, transversely isotropic, hexahedral and octahedral interface orientation distributions (IOD). The estimates are in accordance with well-established analytical results such as the Hashin–Shtrikman bounds and Hill’s findings for phases with equal shear moduli.For isotropic and transversely isotropic IODs, this approach is compared to the Hashin–Shtrikman bounds and the inclusion-based self-consistent approach. At extremal volume fractions, both approaches coincide up to first order with complementary and mixed Hashin–Shtrikman-bounds. Thus, our approach provides an alternative to the self-consistent approach.Moreover, the effective stiffness inherits any symmetry of the IOD. Therefore, it captures basic features of the morphology-induced anisotropy.For the hexahedral and octahedral IOD, the approach is compared to RVE simulations. To assess the impact of morphological features beyond the IOD, we consider RVEs with different microstructures but equal IOD. Comparing similar microstructures, the error attains a local minimum close to the point of equal arrangement of phases. Further, we find a reasonable agreement if the shear moduli are of the same order of magnitude or if both phases percolate the material.

Rigorous theory of molecular orientational nonlinear optics

Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented.

Elastic Properties of a Polymer/Silicate Composite with Platelike Multilayer Filler Particles

A variant of stepwise calculations of the elastic constants of a composite containing platelike multilayer filler particles is presented. First, the effective characteristics of unexfoliated particles in the form of multilayer stacks with interlaminar galleries enlarged as a result of intercalation of polymer are determined. Then, the independent elastic constants of the transversely isotropic representative structural elements of a composite in which multilayer particles are located strictly coplanarly, i.e., parallel to each other, are calculated. Finally, the elastic constants of a composite with randomly oriented particles are obtained by using the method of orientational averaging. Data on the influence of the number of monolayers in the unexfoliated silicate filler particles on their reinforcing efficiency are reported and discussed.

Influence of void microstructure on the effective elastic properties of discontinuous fiber-reinforced composites

This study investigates the influence of void microstructure on the effective elastic properties of high fiber volume fraction discontinuous fiber-reinforced composites with randomly oriented fibers. A void microstructure is characterized by using parameters such as the number of voids, void volume fraction, void Aspect Ratio and void size distribution. In order to overcome the difficulties associated with the creation of high fiber volume fraction representative volume element models containing voids, a novel automation program called “ArtiComp” is developed. This program is used to generate representative volume element models of discontinuous fiber-reinforced composites containing randomly oriented straight fibers, curved fibers and spheroidal voids. The effective properties of discontinuous fiber-reinforced composites are computed using a finite element-based micromechanics approach. For comparison, the Mori-Tanaka method is used to compute the effective properties of unidirectional discontinuous fiber-reinforced composites and then orientation averaging is performed on these properties to obtain the effective properties of discontinuous fiber-reinforced composites with randomly oriented fibers. The comparison shows that the finite element predicted properties are stiffer than the analytically predicted properties. The results indicate that the finite element predicted properties are dependent on the number of voids used to represent the void volume. It is seen that the effective properties significantly decrease when void volume fraction is increased. The void Aspect Ratio and void size distribution are found to have a negligible influence on the effective properties. Finally, it is observed that straight fiber composites with voids perform better than the corresponding curved fiber composites with voids.