Mesoscopic Heterogeneities Research Articles

A material combination principle for highly efficient polymer solar cells investigated by mesoscopic phase heterogeneity

Organic solar cells have become a promising energy conversion candidate because of their unique advantages. Novel fullerene derivatives, as a common acceptor, can increase power conversion efficiency (PCE) by increasing the open-circuit voltage. As a representative acceptor, Indene-C60 bisadduct (ICBA) can reach high efficiency with poly(3-hexylthiophene) (P3HT). On the other hand, the novel synthesized polymers mainly aimed to broaden the optical absorption range have steadily promoted efficiency to higher than 9%. However, it is challenging to obtain the desired result by simply combining ICBA with other high-efficiency donors. Thus, P3HT or a high-efficiency polymer PBDTTT-C-T (copolymer of thienyl-substituted BDT with substituted TT) is used as donor and PCBM or ICBA as acceptor in this article to clarify the mechanism behind these materials. The optical and photovoltaic properties of the materials are studied for pair-wise combination. Among these four material groups, the highest PCE of 6.2% is obtained for the PBDTTT-C-T/PCBM combination while the lowest PCE of 3.5% is obtained for the PBDTTT-C-T/ICBA combination. The impact of the mesoscopic heterogeneity on the local mesoscopic photoelectric properties is identified by photo-conductive AFM (pc-AFM), and the consistence between the mesoscopic properties and the macroscopic device performances is also observed. Based on these results, an interface combined model is proposed based on the mesoscopic phase heterogeneity. This study provides a new view on the rational selection of photovoltaic materials, where, aside from the traditional energy level and absorption spectrum matching, the matching of mesoscopic heterogeneity must also be considered.

A crystal-plasticity FEM study on effects of simplified grain representation and mesh types on mesoscopic plasticity heterogeneities

A numerical study using crystal plasticity finite element method was performed in order to investigate the influence of the grain boundary morphology (stair-case or smooth/flat) and the selection of different mesh types (hexahedral and tetrahedral meshes) on the distribution of simulated plasticity heterogeneities. A bicrystal (a hard grain and a soft grain) sphere embedded in a cubic grain was utilized to perform the current numerical study. The volume averaged responses for the simulated plasticity values (von Mises stress, total accumulated slip system shear and maximum accumulated slip system shear) showed no significant dependence on the grain boundary representation and mesh type. However, the bicrystal represented by uniform hexahedral meshes with stair-case grain boundaries tends to show more extreme local plasticity values (in the head and tail of the distribution), particularly populated in the grain boundary region. Differences in local plasticity values between the stair-case and the smooth (or flat) grain boundary cases and between the hexahedral and the tetrahedral mesh cases were largest in the grain boundary region, and the degree of the differences depended upon the plasticity susceptibility of the grain. The simulation results suggest that the grain boundary represented by the stair-case morphology can be a source and/or a sink for local extreme plasticity, compared to the grain boundary represented by the smooth (or flat) morphology.

Impact on multi-layered polypropylene foams

Foams, and particularly the polypropylene foam, are more and more often used in the area of injury protection and passive safety for its energy absorption capacity. This multi-scale material is constituted of mesoscopic beads with a large variability of the material properties. To study the effects of these mesoscopic heterogeneities on both the macroscopic and the local behaviors, numerical simulations on virtual volumes of foam under dynamic loading have been performed. The influence of the organized system of heterogeneities has also been studied in the cases of a random distribution and a multi-layered volume. Experimental dynamic compressive tests have been performed on multi-layered volumes of foam and compared with the results of the Finite Element Method.

Sample dilation and fracture in response to high pore fluid pressure and strain rate in quartz‐rich sandstone and siltstone

Natural hydraulic fractures (NHFs) are inferred to form where pore pressure exceeds the least compressive stress by an amount equal to the tensile strength of the rock. We improved upon an experimental protocol that meets the NHF criterion within cylindrical samples with the most tensile effective stress parallel to the sample axis. The effective tensile stresses achieved during these experiments ranged from 17–47 MPa. The pore fluids used had higher viscosities than water and the axial strain rate was rapid (∼10−3s−1) to delay dissipation of fluid pressure by flow. Four experiments on St. Peter Sandstone samples and two on an Abo Formation siltstone sample were performed under these conditions and under drained conditions. None of the drained experiments resulted in failure, but all of the sandstone and one of the siltstone samples fractured in response to elevated pore pressures. Consistent with field and theoretical studies, mechanical heterogeneity was a first order control on fracture location. In the absence of mesoscopic heterogeneity, fracture location coincided with the maximum pore pressure. Samples responded to elevated pore pressures and differential stresses by dilating, the magnitude of which was sufficient to achieve atmospheric pore pressure. Samples failed 2 to 250 s after experiencing the greatest pore pressures, when the effective stresses were no longer tensile. Thus, the high pore pressures and effective tensile stresses experienced early in the experiments were sufficient to fracture the rocks, even though they were not sustained until failure. These results provide insight into processes of fluid‐driven fracture formation.

Dynamic indentation on layered polypropylene foams

Foams, and particularly the polypropylene foam, are more and more often used in the area of injury protection and passive safety for its energy absorption capacity. This multi-scale material is constituted of mesoscopic beads with a large variability of the material properties. First, to study the effects of these mesoscopic heterogeneities on both the macroscopic and the local behaviors, numerical simulations on virtual volumes of foam under dynamic loading have been performed. The influence of the organized system of heterogeneities has also been studied in the cases of a random distribution and a multi-layered volume. Experimental dynamic compressive tests have been performed on multi-layered volumes of foam and compared with the results of the Finite Element Method. Second, indentation experiments have also been performed using a cylindrical shape indenter.

Influence of mesoscopic heterogeneity on macroscopic behaviour of rock failure of large-scale samples

Using RFPA soft code, influence of mesoscopic heterogeneity and randomness on behaviour of rock failure of large-scale samples is analysed. Results show that the failure of big-scale samples is manifested as brittle failure, even if the coefficient of homogeneity is 1, the curve after peak load has no gentle evidence, it is obviously different to the research results of small-scale samples. The comparative study when the coefficient of homogeneity m is respectively 1 and 5 shows that, when the coefficient of homogeneity is low, many cracks extending simultaneous and connecting mutually and finally a macroscopic transfixion crack is formed. When the coefficient of homogeneity is high, it extends according to single crack. The localisation phenomenon of failure is even obvious in large-scale samples with the increasing of coefficient of homogeneity, the stress stacking which formed in the cracks extending can easily cause sufficient failure in local area. With the increasing of sample size, the mechanical behaviour effect which caused by randomness can been decreased.

Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks

SUMMARY Using a numerical approach, we explore wave-induced fluid flow effects in partially saturated porous rocks in which the gas–water saturation patterns are governed by mesoscopic heterogeneities associated with the dry frame properties. The link between the dry frame properties and the gas saturation is defined by the assumption of capillary pressure equilibrium, which in the presence of heterogeneity implies that neighbouring regions can exhibit different levels of saturation. To determine the equivalent attenuation and phase velocity of the synthetic rock samples considered in this study, we apply a numerical upscaling procedure, which permits to take into account mesoscopic heterogeneities associated with the dry frame properties as well as spatially continuous variations of the pore fluid properties. The multiscale nature of the fluid saturation is taken into account by locally computing the physical properties of an effective fluid, which are then used for the larger-scale simulations. We consider two sets of numerical experiments to analyse such effects in heterogeneous partially saturated porous media, where the saturation field is determined by variations in porosity and clay content, respectively. In both cases we also evaluate the seismic responses of corresponding binary, patchy-type saturation patterns. Our results indicate that significant attenuation and modest velocity dispersion effects take place in this kind of media for both binary patchy-type and spatially continuous gas saturation patterns and in particular in the presence of relatively small amounts of gas. The numerical experiments also show that the nature of the gas distribution patterns is a critical parameter controlling the seismic responses of these environments, since attenuation and velocity dispersion effects are much more significant and occur over a broader saturation range for binary patchy-type gas–water distributions. This analysis therefore suggests that the physical mechanisms governing partial saturation should be accounted for when analysing seismic data in a poroelastic framework. In this context, heterogeneities associated with the dry frame properties, which do not play important roles in wave-induced fluid flow processes per se, should be taken into account since they may determine the kind of gas distribution pattern taking place in the porous rock.

Construction of a disorder variable from Steinhardt order parameters in binary mixtures at high densities in three dimensions

Using molecular dynamics simulation, we investigate the structural disorder in crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of N(1) + N(2) = 4096 particles at a low temperature in three dimensions. The size ratio σ(2)/σ(1) between the large and small particles is either 1.2 or 1.4. The crossovers among these states occur, as the composition of the large particles c = N(2)/(N(1) + N(2)) is varied. We define a disorder variable D(j) for each particle j in terms of local bond order parameters based on spherical harmonics (Steinhardt order parameters). Stacking faults and grain boundaries in fcc polycrystal and mesoscopic structural heterogeneity in glass are then visualized. At small c, disturbances of large particles is stronger for larger σ(2)/σ(1). At large c, the transition between glass and polycrystal occurs nearly discontinuously at c = c(c) ~ 0.8. At σ(2)/σ(1) = 1.4, microphase separation occurs in polycrystal states with c > c(c), where fcc crystal grains comprising the large particles are enclosed by amorphous layers composed of the two particle species.

Time-lapse sonic logs reveal patchy CO2saturation in-situ

[1] Based on time-lapse sonic and neutron porosity logs from the Nagaoka CO2 sequestration experiment, a P-wave velocity-saturation relation at reservoir depth is retrieved. It does not coincide with either of the end-member models of uniform and patchy saturation but falls in between even if realistic error estimates for the host rock properties are considered. Assuming a random distribution of CO2 patches it is shown that the mechanism of wave-induced flow can be evoked to explain this velocity-saturation relation. Characteristic CO2 patch size estimates range from 1 to 5 mm. Such mesoscopic heterogeneity can be responsible for attenuation and dispersion in the well logging frequency band.

Mesoscale modelling of concrete for static and dynamic response analysis -Part 2: numerical investigations

As a brittle and heterogeneous material, concrete behaves differently under different stress conditions and its bulk strength is loading rate dependent. To a large extent, the varying behavioural properties of concrete can be explained by the mechanical failure processes at a mesoscopic level. The development of a computational mesoscale model in a general finite element environment, as presented in the preceding companion paper (Part 1), makes it possible to investigate into the underlying mechanisms governing the bulk-scale behaviour of concrete under a variety of loading conditions and to characterise the variation in quantitative terms. In this paper, we first present a series of parametric studies on the behaviour of concrete material under quasi-static compression and tension conditions. The loading-face friction effect, the possible influences of the non-homogeneity within the mortar and ITZ phases, and the effect of randomness of coarse aggregates are examined. The mesoscale model is then applied to analyze the dynamic behaviour of concrete under high rate loading conditions. The potential contribution of the mesoscopic heterogeneity towards the generally recognized rate enhancement of the material compressive strength is discussed.

Effect of heterogeneity on mechanical and acoustic emission characteristics of rock specimen

The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods. Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks. The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC3D software. Five schemes were adopted to investigate the influence of heterogeneity. The results demonstrate that as the homogeneity increases, the peak strength and brittleness of rocks increase, and the macro elastic modulus improves as well. Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0. The volume expansion is not so obvious when the homogeneity increases. As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock. When the homogeneity coefficient is high, the cumulative acoustic emission events-axial strain curve is gentle before the rock failure. The numerical results agree with the previously numerical results and earlier experimental measurements.

Comparative study of four failure criteria for intact bedded rock salt

Damage smear method (DSM) is adopted to study trans-scale progressive rock failure process, based on statistical meso-damage model and finite element solver. The statistical approach is utilized to reflect the mesoscopic rock heterogeneity. The constitutive law of representative volume element (RVE) is established according to continuum damage mechanics in which double-damage criterion is considered. The damage evolution and accumulation of RVEs are used to reveal the macroscopic rock failure characteristics. Each single RVE will be represented by one unique element. The initiation, propagation and coalescence of meso-to macro-cracks are captured by smearing failed elements. The above ideas are formulated into the framework of the DSM and programed into self-developed rock failure process analysis (RFPA) software. Two laboratory-scale examples are conducted and the well-known engineering-scale tests, i.e. Atomic Energy of Canada Limited's (AECL's) Underground Research Laboratory (URL) tests, are used for verification. It shows that the simulation results match with other experimental results and field observations.

Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below [Formula: see text], the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot’s theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot’s equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

Facies architecture and heterogeneity of the fluvial–aeolian reservoirs of the Sergi formation (Upper Jurassic), Recôncavo Basin, NE Brazil

The Sergi Formation (Upper Jurassic) represents the main hydrocarbon reservoir of the Recôncavo Basin, Brazil. The basal vertical facies succession of the Sergi Formation comprises reservoirs formed by a complex fluvio–aeolian–lacustrine interaction. Facies architecture and detailed petrophysical analysis of these reservoirs have enhanced the understanding of heterogeneity at a variety of scales and has allowed the development of predictive models that describes the range of styles of mixed fluvial–aeolian reservoirs. At megascopic scale, the reservoirs are predominantly composed of sand bodies deposited by fluvial channel and aeolian facies associations. Regional flooding surfaces and sequence boundaries are their main flow barriers. The regional flooding surfaces are composed of fine-grained sediments deposited by lacustrine facies associations and the sequence boundaries act as flow barriers due to mechanically infiltrated clays. Based on its geometrical relations, reservoirs linked to fluvial–aeolian–lacustrine interaction formed two types of reservoirs at macroscopic scale: (i) with good lateral continuity of aeolian packages and relatively simple stratigraphic correlation and (ii) of highly compartmentalized aeolian packages with complex stratigraphic correlation and truncation by fluvial deposits. Mesoscopic heterogeneity reflects lithofacies, sedimentary structures, and lamina-scale variability within aeolian and fluvial facies associations.

Direct evidence of mesoscopic dynamic heterogeneities at the surfaces of ergodic ferroelectric relaxors

Spatial variability of polarization relaxation kinetics in relaxor ferroelectric 0.9Pb(Mg1/3Nb2/3)O3-0.1PbTiO3 is studied using time-resolved Piezoresponse Force Microscopy. Local relaxation attributed to the reorientation of polar nanoregions is shown to follow stretched exponential dependence, exp(-(t/tau)^beta), with beta~~0.4, much larger than the macroscopic value determined from dielectric spectra (beta~~0.09). The spatial inhomogeneity of relaxation time distributions with the presence of 100-200 nm "fast" and "slow" regions is observed. The results are analyzed to map the Vogel-Fulcher temperatures on the nanoscale.

Spatial distribution of relaxation behavior on the surface of a ferroelectric relaxor in the ergodic phase

Spatial homogeneity of polarization relaxation behavior on the surface of 0.9Pb(Mg1/3Nb2/3)O3–0.1PbTiO3 crystals in the ergodic relaxor phase is studied using three-dimensional time-resolved spectroscopic piezoresponse force microscopy. The number of statistically independent components in the spectroscopic image is determined using principal component analysis. In the studied measurement time interval, the spectra generally exhibit logarithmic behavior with spatially varying slope and offset, and the statistical distribution of these parameters are studied. The data illustrate the presence of mesoscopic heterogeneity in the dynamics of the relaxation behavior that can be interpreted as spatial variation in local Vogel–Fulcher temperatures.

A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media

An important loss effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger than the pore size but much smaller than the predominant wavelengths of the fast compressional and shear waves. These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patches of gas induces a smaller fluid-pressure in the gas patches than in the water-saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas–water interfaces generating significant energy losses and velocity dispersion. To perform numerical simulations using Biot’s equations of motion, it would be necessary to employ extremely fine meshes to properly represent these mesoscopic heterogeneities and their attenuation effects on the fast waves. An alternative approach to model wave propagation in these type of Biot media is to employ a numerical upscaling procedure to determine effective complex P-wave and shear moduli defining locally a viscoelastic medium having in the average the same properties than the original Biot medium. In this work the complex P-wave and shear moduli in heterogeneous fluid-saturated porous media are obtained using numerical gedanken experiments in a Monte Carlo fashion. The experiments are defined as local boundary value problems on a reference representative volume of bulk material containing stochastic heterogeneities characterized by their statistical properties. These boundary value problems represent compressibility and shear tests needed to determine these moduli for a given realization. The average and variance of the phase velocities and quality factors associated with these moduli are obtained by averaging over realizations of the stochastic parameters. The Monte Carlo realizations were stopped when the variance of the computed quantities stabilized at an almost constant value. The approximate solution of the local boundary value problems was obtained using a Galerkin finite element procedure, and the method was validated by reproducing known solutions in the case of periodic layered media. For the spatial discretization, standard bilinear finite element spaces are employed for the solid phase, while for the fluid phase the vector part of the Raviart–Thomas–Nedelec mixed finite element space of order zero was used. Results on the uniqueness of the continuous and discrete problems as well as optimal a priori error estimates for the Galerkin finite element procedure are derived. Numerical experiments showing the implementation of the procedure to estimate the average and variance of the fast compressional and shear phase velocities and inverse quality factors in these kind of highly heterogeneous fluid-saturated porous media are presented.

Transient solution for viscoacoustic wave propagation in a double porosity medium, and its limitations

It is well known that Biot theory (Biot, 1956;1962) of porous-media acoustics ignores all wave-induced flow at mesoscopic scales, i.e. scales greater than the grain size but less that the wavelength. Biot?s theory can not explain high level attenuation observed in natural porous media such as fluid-filled sands or sandstone over the seismic frequency range ( 10- 200 Hz). This attenuation is successfully described by the mesoscopic heterogeneity models (e.g., Gurevich and Lopatnikov, 1995; Gelinksy and Shapiro, 1997; Johnson, 2001). By applying the volume averaging theory to the local Biot poroelastic law, Pride an Berryman (2003a,b) developed the double-porosity, dual permeability (DPDP) model It gives a theoretical framework, including the field equations governing the linear acoustics of composites with two isotropic porous constituents (phase 1 and phase 2), to model acoustic wave propagation through heterogeneous porous structures. Under the assumption that phase 2 is entirely embedded in phase 1, the double-porosity theory is reduced to the effective Biot theory with the complex frequency-dependent elastic moduli in which the internal mesoscopic flow is incorporated. This theory provides good agreement with measurements of attenuation over the seismic and ultrasonic frequency bands (Pride et al., 2004). In this paper, the analytical transient solution and dispersion characteristics for the double-porosity model are obtained over the whole frequency range for a homogeneous medium. A homogeneous poro-viscoacoustic model is constructed and analytically solved to approximate the double porosity model. The comparison between the results of the two models shows the likely validity and limitations of numerical solutions using a poro-viscoacoustic model to represent a double porosity medium in the heterogeneous case. Our calculations show that the dissipation by local mesoscopic flow of the double porosity model is very hard to fit over the entire frequency range by a single Zener element. We choose the relaxation function which just approximates the dispersion behaviour of the double porosity model around the source centre frequency. It is shown that if the frequency is much lower than the peak attenuation frequency of the double porosity model, then wave propagation can be well described by the poro-viscoacoustic model with a single Zener element. For most water-filled sandstones having a double porosity structure, this holds true across the seismic frequency range.

Structural polymorphism in heterogeneous cytoskeletal networks

The viscoelastic response of living cells is largely determined by heterogenous networks of cross-linked and bundled actin filaments. The quantitative impact of such local network heterogeneities is studied best in well-defined in vitro model systems by employing microscopic and micromechanical techniques. In this study, we show that reconstituted α-actinin/actin networks exhibit a structural polymorphism, which is dictated by two types of mesoscopic heterogeneities: a composite bundle phase at intermediate α-actinin concentrations and clusters of actin bundles at high α-actinin concentrations. We demonstrate the influence of these structural heterogeneities on the mechanical properties of cross-linked and bundled actin networks. First, locally embedding stiff bundles into the network strengthens the macroscopic network response. Second, the formation of fractal, star-like bundle clusters drastically concentrates material in localized spots and weakens the network elasticity. Such bundle cluster networks exhibit kinetically trapped and thus metastable network configurations—which is contrary to the commonly accepted belief of equilibrated network formations.

Seismic attenuation in porous rocks with random patchy saturation

ABSTRACTSaturation of porous rocks with a mixture of two fluids has a substantial effect on seismic‐wave propagation. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves due to the mechanism of wave‐induced fluid‐flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a regular way. However, recent experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Based on an approximation for the coherent wavefield in random porous media, we develop a model which assumes a continuous distribution of fluid heterogeneities. As this continuous random media approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental data. We also show how to relate the random functions to experimentally measurable parameters.