Isotropic Aggregates Research Articles

Computational homogenization of the elastic properties of polycrystalline fcc metals within Mindlin’s second strain-gradient theory

The lack of interest in Mindlin’s second strain-gradient theory, despite its success in characterizing various phenomena for which there is no explanation in the classical elasticity, is predominantly due to the numerous higher-order elastic constants involved therein. As an attempt to overcome this shortcoming, a computational homogenization method for determining such elastic constants of polycrystalline face-centered cubic (fcc) metals is proposed in the present study. In this homogenization method, using the Voigt-type averaging scheme, a polycrystalline material is modeled by an isotropic aggregate of randomly oriented single crystals without accounting for the grain size effect and the complexities due to grain boundaries and junctions. Subsequently, analytical expressions for the strain energy due to certain modes of loading are determined, and molecular simulations of a few fcc metals under such modes of loading are performed. Then, by fitting the corresponding analytical expressions to the results obtained from these simulations, the effective elastic constants and consequently the effective characteristic lengths of the fcc metals in their polycrystalline form are determined. Moreover, the free-surface-induced reconstruction in a thin layer of a solid is addressed both analytically and by molecular simulations, as a result of which the effective moduli of cohesion of the fcc metals in their polycrystalline form are calculated. In addition, the complete set of conditions for the positive-definiteness of the strain-energy-density function of isotropic materials within the adopted theory is derived, and subsequently a discussion of whether or not the numerical values obtained for the effective elastic moduli of the polycrystalline fcc metals satisfy such conditions is provided.

Young's modulus of the different crystalline phases of poly (l-lactic acid)

Young's modulus of α′- and α-crystals of poly (l-lactic acid) (PLLA), more precisely, of aggregates of isotropically arranged lamellae, has been estimated based on dynamic-mechanical analysis of sets of isotropic film samples containing largely different though well-defined amounts of crystals. Evaluation of the modulus of elasticity of these film samples yielded the dependence of Young's modulus as a function of the enthalpy-based crystallinity, increasing with the crystal fraction in the assessed range, from zero to about 75% crystallinity. Extrapolation towards 100% crystallinity suggests values of Young's modulus of around 3.7 and 4.6 GPa for isotropic aggregates of α′- and α-crystals, respectively, being only slightly higher than the modulus of the unaged glassy amorphous phase of 3.0 GPa. Noting the inherent anisotropy of the crystal modulus, suggested in the literature, the average modulus determined in this work seems to be controlled by weaker interchain secondary bonding but not the modulus in chain direction. Great effort has been undertaken to minimize errors by keeping the lamellar thickness in samples of different crystallinity constant, and by providing evidence for independence of the moduli on the spherulitic superstructure.

Effect of asphaltene adsorption on the magnetic and magnetorheological properties of heavy crude oils and Fe3O4 nanoparticles systems

An essential understanding of the adsorptive phenomena involving nanomaterials and asphaltenes has received considerable attention in oil recovery and production applications. Particularly, iron oxide-based nanoparticles have emerged as advanced materials due to their unique physicochemical properties, including thermal conductivity and superparamagnetism. On this basis, the kinetics and adsorption isotherms of magnetite (Fe3O4) nanoparticles/asphaltene systems were investigated, as well as the synergistic effect of resins acting as stabilizing colloidal agents. The results indicated rapid asphaltene adsorption that, essentially, follows the phenomenological external mass transfer (EMT) model. At the equilibrium, the asphaltene adsorption was adequately described by the monolayer Langmuir model. By these findings, it was studied for the first time the effect of the adsorbed asphaltenes on the magnetic dipolar interactions in nanoparticles/asphaltene powder state configurations, by applying a simple analytical model based on magnetic susceptibility and demagnetizing field concepts. It was proven accurately that asphaltenes coated the surfaces of the nanoparticles forming layers that stimulate a steric repulsive barrier between particles and, thus, reducing the intensity of interactions. Accordingly, a theoretical method was validated to estimate the magnetic-size distribution parameters by comparison with the physical distribution data obtained by Transmission Electron Microscopy (TEM). Finally, from the magnetically modified dynamic rheological properties, it was inferred that isotropic aggregates are naturally formed in the absence of the magnetic field, and these morphological features were not dramatically changed after the imposition of the field, leading to direct extrapolation of the modeling-based procedure for powders to real colloidal configurations applied in oil field operations.

On analytical estimates of the effective elastic properties of polycrystalline silicon

Several analytical approaches can be utilized to estimate the elastic properties of polycrystalline silicon. In experimental studies, the notion of an macroscopically isotropic aggregate is introduced while the single crystals obey cubic symmetry. We here give a synopsis on analytical approaches to predict elastic properties and apply them to estimate effective parameters of polycrystalline silicon. Here, the predictions are based on the parameters associated with shear solely. The results are juxtaposed in terms of the approaches applied, while different measures are introduced for evaluation. In comparison with experimental findings, the geometric mean implies a reasonable estimation for the elastic properties of polycrystalline silicon.

Statistical analysis of chloride concentration distribution in concrete by a meso-scale model considering irregular shape aggregates

The purpose of this paper is to investigate the probabilistic characteristics of chloride concentration distribution in concrete with irregular aggregates by a numerical method. Chloride diffusion was simulated based on a three-dimensional geometrical model considering random distribution of irregular aggregate particles. The simulated results indicated that the chloride diffusivity increased as the aggregate sphericity and flatness ratio increased. The standard deviation of chloride concentration at the same depth could be decreased by using aggregates with a higher sphericity or a more isotropic aggregate. The heterogeneity of the concrete’s meso-structure should be considered for evaluation of the critical time in steel corrosion in concrete under chloride environment. Critical time dispersion could by decreased by using aggregates with higher sphericity. The concrete cover thickness was designed considering the spatial variability of critical chloride front. This research confirms that the spatial variability of aggregate distribution should be considered if maximum critical chloride depths were used as the cover thickness.

Collagen polarization promotes epithelial elongation by stimulating locoregional cell proliferation.

Epithelial networks are commonly generated by processes where multicellular aggregates elongate and branch. Here, we focus on understanding cellular mechanisms for elongation using an organotypic culture system as a model of mammary epithelial anlage. Isotropic cell aggregates broke symmetry and slowly elongated when transplanted into collagen 1 gels. The elongating regions of aggregates displayed enhanced cell proliferation that was necessary for elongation to occur. Strikingly, this locoregional increase in cell proliferation occurred where collagen 1 fibrils reorganized into bundles that were polarized with the elongating aggregates. Applying external stretch as a cell-independent way to reorganize the extracellular matrix, we found that collagen polarization stimulated regional cell proliferation to precipitate symmetry breaking and elongation. This required β1-integrin and ERK signaling. We propose that collagen polarization supports epithelial anlagen elongation by stimulating locoregional cell proliferation. This could provide a long-lasting structural memory of the initial axis that is generated when anlage break symmetry.

Single Crystal Elastic Properties of Hemimorphite, a Novel Hydrous Silicate

Hemimorphite, with the chemical formula Zn4Si2O7(OH)2·H2O, contains two different types of structurally bound hydrogen: molecular water and hydroxyl. The elastic properties of single-crystal hemimorphite have been determined by Brillouin spectroscopy at ambient conditions, yielding tight constraints on all nine single-crystal elastic moduli (Cij). The Voigt–Reuss–Hill (VRH) averaged isotropic aggregate elastic moduli are KS (VRH) = 74(3) GPa and μ (VRH) = 27(2) GPa, for the adiabatic bulk modulus and shear modulus, respectively. The average of the Hashin–Shtrickman (HS) bounds are Ks (HS) = 74.2(7) GPa and and μ (HS) = 26.5(6) GPa. Hemimorphite displays a high degree of velocity anisotropy. As a result, differences between upper and lower bounds on aggregate properties are large and the main source of uncertainty in Ks and μ. The HS average P wave velocity is VP = 5.61(4) km/s, and the HS S-wave velocity is VS = 2.77(3) km/s. The high degree of elastic anisotropy among the on-diagonal longitudinal and pure shear moduli of hemimorphite are largely explained by its distinctive crystal structure.

Nonlinearly Elastic Constitutive Relation of Anisotropic Aggregate of Cube Crystallites

Under Voigt model, Barsch and Johnson gave the formula of nonliearly elastic constitutive relations for isotropic aggregates of cubic crystallites and orthorhambic aggregates of cubic crystallies, respectively. In this paper, a nonlinear elastic constitutive relation based on Voigt model, which is more general than Barsch's and Johnson's results, is derived for the set of anisotropic cubic grains. The anisotropy of metals is described by the texture coefficient.

Lattice Thermal Conductivity of MgSiO3 Postperovskite Under the Lowermost Mantle Conditions From Ab Initio Anharmonic Lattice Dynamics

AbstractThe lattice thermal conductivity (κlat) of MgSiO3 postperovskite (Mg‐PPv) under the lowermost mantle pressure (P) and temperature (T) conditions was calculated using density functional theory combining anharmonic lattice dynamics theory. The κlat of Mg‐PPv was found to be ~50% higher than that of MgSiO3 bridgmanite (Mg‐Brg) owing to the larger phonon group velocity and lifetime. The lateral variation in the core‐mantle boundary heat flux (qCMB) can be enhanced by the Brg‐PPv phase transition. We also found that the κlat along the c axis of Mg‐PPv is close to the conductivity of isotropic aggregate. This suggests that the effect of anisotropy in the κlat on qCMB would be minor if the transversely isotropic aggregate with the c axis vertical alignment, a potential source of seismic anisotropy in the D″ layer, is developed.

Nearly Isotropic Conjugated Polymer Aggregates with Efficient Local Exciton Diffusion

To bridge the gap between single-molecule and bulk thin film studies of organic semiconductors and understand the influence of molecular structure on photophysical properties across scales, we prepared and characterized aggregates containing a few to more than a thousand single chains via well-controlled solvent vapor swelling of an inert polymeric matrix containing the conjugated polymer poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV). The single chains were initially immobilized in conformations with few interchain contacts, which can support exciton funneling on the single-molecule level. We show that aggregates prepared via solvent swelling and templated on such molecules result in largely isotropic aggregates. Analysis of aggregate polarization anisotropy, photoluminescence transient decay, and photoluminescence spectra as a function of aggregate size suggests that in these aggregates exciton diffusion is locally enhanced upon initial aggregation but does not reach extended length...

Poisson's Ratio and Auxetic Properties of Natural Rocks

AbstractHere we provide an appraisal of the Poisson's ratios (υ) for natural elements, common oxides, silicate minerals, and rocks with the purpose of searching for naturally auxetic materials. The Poisson's ratios of equivalently isotropic polycrystalline aggregates were calculated from dynamically measured elastic properties. Alpha‐cristobalite is currently the only known naturally occurring mineral that has exclusively negative υ values at 20–1,500°C. Quartz and potentially berlinite (AlPO4) display auxetic behavior in the vicinity of their α‐β structure transition. None of the crystalline igneous and metamorphic rocks (e.g., amphibolite, gabbro, granite, peridotite, and schist) display auxetic behavior at pressures of >5 MPa and room temperature. Our experimental measurements showed that quartz‐rich sedimentary rocks (i.e., sandstone and siltstone) are most likely to be the only rocks with negative Poisson's ratios at low confining pressures (≤200 MPa) because their main constituent mineral, α‐quartz, already has extremely low Poisson's ratio (υ = 0.08) and they contain microcracks, micropores, and secondary minerals. This finding may provide a new explanation for formation of dome‐and‐basin structures in quartz‐rich sedimentary rocks in response to a horizontal compressional stress in the upper crust.

Nonlinear elastic properties of the polycrystalline refractory metals at Megabar pressures: Theoretical approach

We present the theoretical technique for the calculation of nonlinear elastic properties of polycrystals in the presence of hydrostatic pressure. For the isotropic aggregates of single-crystal grains with cubic or hexagonal structures at given pressure we define the Lamé constants and express them through the second and third order single-crystal elastic constants. We present the calculated third order Lamé elastic modules of polycrystalline W, Mo and Ru in the pressure range of 0–600GPa. The results agree with available experimental data. The obtained values can be used for the prediction of properties for these materials at high pressures and finite deformations. We show, that the methodology can be effectively used with ab initio calculations techniques to obtain the data on elastic properties of practical importance.

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.

Viscous anisotropy of textured olivine aggregates, Part 1: Measurement of the magnitude and evolution of anisotropy

The development of crystallographic textures in olivine-rich rocks leads to a marked anisotropy in viscosity of the upper mantle, strongly influencing a variety of large-scale geodynamic processes. Most estimates of the magnitude of viscous anisotropy in the upper mantle are derived from micromechanical models that predict textural and mechanical evolution numerically. Unfortunately, relatively few data exist with which to benchmark these models, and therefore their applicability to geodynamic processes remains in question. Here we present the results from a series of laboratory deformation experiments that yield insight into the magnitude and evolution of the anisotropy of olivine aggregates during deformation along complex loading paths. Aggregates of Fo50 olivine were first deformed in extension in a gas-medium apparatus at a temperature of 1473 K, confining pressure of 300 MPa, and a variety of stresses and strain rates. Early in the extension experiments, samples exhibited viscosities similar to those previously determined for isotropic aggregates. Extensional deformation was accompanied by formation of crystallographic textures with [100] axes dominantly aligned with the extension axis. Samples were subsequently deformed in torsion under similar conditions to shear strains of up to 15.5. Early in the torsion experiments, samples supported stresses a factor of ∼2 larger than measured at the end of extension experiments, demonstrating a marked anisotropy in viscosity. Textures at the end of torsion experiments exhibited [100] axes dominantly aligned with the shear direction, comparable to previous experimental observations. Evolution of the textures resulting from extension to those resulting from torsion was analyzed through examination of radial sections of torsion samples. Our results confirm that texture produces viscous anisotropy in olivine aggregates, and we provide a simple, calibrated parameterization of viscous anisotropy for use in geodynamic models. Our results also provide an extensive dataset for future calibration of micromechanical models that track the evolution of anisotropy in upper mantle rocks.

Particle-directed assembly of semiflexible polymer chains.

We use Langevin dynamics simulations to study aggregation of semiflexible polymers driven by attractions between polymers and spherical particles. We consider a simple model with purely repulsive polymer/polymer and particle/particle interactions but attractive polymer/particle interactions. We find a rich "phase diagram" that contains several different types of globular and rod-like aggregates with either liquid-like or crystalline structure for the particle positions. Systems that exhibit rod-like aggregates with crystalline internal order exhibit a discontinuous rod-globule transition, while systems with liquid-like internal order exhibit a smooth crossover between isotropic and elongated aggregates with increasing chain stiffness. Polymers in elongated liquid-like aggregates often adopt helical configurations that wind around the axis of the aggregate.

Relative stability and contrasting elastic properties of serpentine polymorphs from first‐principles calculations

AbstractWe conduct first‐principles calculations to determine the relative stability field and elasticity contrast of serpentine polymorphs at pressure and temperature conditions relevant to the oceanic lithosphere and subduction zone. At high pressures (>4 GPa), the corrugated form of serpentine polymorph (antigorite, Atg) plus brucite (Brc) assemblage is thermodynamically more favorable compared to its planar counterpart (lizardite, Liz). The phase boundary between Liz and Atg + Brc exhibits a negative slope in the whole P‐T range, indicating that this transition can be driven by increasing either pressure or temperature. Near 0 GPa, the slope is about −33 K/GPa. As pressure exceeds 1 GPa, the transition temperature starts to decrease more rapidly. Because of the corrugated nature of its constituent layers, Atg is more susceptible to intralayer deformations (7 to 36% smaller C11, C22, C12, and C66 at ambient conditions) while more resistant to interlayer shear deformation (25% larger C44, 36% larger C55) than Liz. In contrast, their responses to the interlayer compressive deformation (C33) are similar. For isotropic polycrystalline aggregates at pressures between 0 and 4 GPa, Atg exhibits a smaller bulk modulus (12 to 15%) and a larger shear modulus (6 to 11%) than Liz, while their density contrast is within 1%. Accordingly, a Liz/Atg transition is accompanied by a decrease in Vp (2 to 3%), an increase in Vs (3 to 5%), and a more pronounced drop in Vp/Vs (6 to 8%). These results may help to identify and characterize serpentine polymorphs produced under various geological settings.

Macroscopic elastic properties of textured ZrN-AlN polycrystalline aggregates: Fromab initiocalculations to grain-scale interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.

Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques

A linear-comparison homogenization technique and its relaxed version are used to compute bounds of the Hashin–Shtrikman and the self-consistent types for the hydrostatic strength of ideally plastic voided polycrystals. Closed-form analytical results are derived for isotropic aggregates of various cubic symmetries (fcc, bcc, ionic). The impact of the variational relaxation on the bounds is found to be significantly larger than that previously observed in fully dense polycrystals. So much so that, quite surprisingly, relaxed self-consistent bounds are found to be weaker than non-relaxed Hashin–Shtrikman bounds in some of the material systems considered.

Elastic properties of six silicate garnet end members from accurate ab initio simulations

The elastic properties of six silicate garnet end members, among the most important rock-forming minerals, are investigated here for the first time via accurate ab initio theoretical simulations. The Crystal program is used, which works within periodic boundary conditions and allows for all-electron basis sets to be adopted. From the computed elastic tensor, Christoffel’s equation is solved along a set of crystallographic directions in order to fully characterize the seismic wave velocity anisotropy in such materials. Polycrystalline isotropic aggregate elastic properties are derived from the computed single-crystal data via the Voigt-Reuss-Hill averaging procedure. Transferability of the elastic properties from end members to their solid solutions with different chemical compositions is also addressed.

Directional sensing by cooperative chemoreceptor arrays modeled as Monod-Wyman-Changeux clusters

Most sensory cells use transmembrane chemoreceptors to detect chemical signals in the environment. The biochemical properties and spatial organization of chemoreceptors play important roles in achieving and maintaining sensitivity and accuracy of chemical sensing. Here we investigate the effects of receptor cooperativity and adaptation on the physical limits for sensing a chemical gradient. We study a single cell with aggregated chemoreceptor arrays on the cell surface and derive a general formula to the limits for gradient sensing from the uncertainty of instantaneous receptor activity. In comparison to independent receptors, we find that cooperativity by nonadaptive receptors could significantly lower the sensing limits in a chemical concentration range determined by the biochemical properties of ligand-receptor binding and ligand-induced receptor activity. Cooperativity by adaptive receptors is beneficial to gradient sensing within a broad range of background concentrations. Our results also show that the isotropic receptor aggregate layout on the cell surface represents an optimal configuration for gradient sensing.