Effective Medium Theory Model Research Articles

Mesoscale characterization of local property distributions in heterogeneous electrodes

The performance of electrochemical devices depends on the three-dimensional (3D) distributions of microstructural features in their electrodes. Several mature methods exist to characterize 3D microstructures over the microscale (tens of microns), which are useful in understanding homogeneous electrodes. However, methods that capture mesoscale (hundreds of microns) volumes at appropriate resolution (tens of nm) are lacking, though they are needed to understand more common, less ideal electrodes. Using serial sectioning with a Xe plasma focused ion beam combined with scanning electron microscopy (Xe PFIB-SEM), two commercial solid oxide fuel cell (SOFC) electrodes are reconstructed over volumes of 126 × 73 × 12.5 and 124 × 110 × 8 μm3 with a resolution on the order of ≈ 503 nm3. The mesoscale distributions of microscale structural features are quantified and both microscale and mesoscale inhomogeneities are found. We analyze the origin of inhomogeneity over different length scales by comparing experimental and synthetic microstructures, generated with different particle size distributions, with such synthetic microstructures capturing well the high-frequency heterogeneity. Effective medium theory models indicate that significant mesoscale variations in local electrochemical activity are expected throughout such electrodes. These methods offer improved understanding of the performance of complex electrodes in energy conversion devices.

Inversion-based method to mitigate noise in borehole sonic logs

A major challenge in the interpretation of seismic measurements and sonic logs is the presence of deleterious noise that impacts the quality and reliability of the estimated seismic wavelets and seismic inversion products. Spatial averaging effects and borehole drilling damage can also bias the estimation of in situ stress and elastic properties from sonic logs. We have developed an inversion-based method to mitigate processing errors, spatial averaging effects, and borehole environmental noise on sonic logs, which does not require arbitrary numerical filters, effective-medium theory models, or time-consuming waveform reprocessing. The inversion-based method estimates layer-by-layer slownesses via joint inversion of shear and compressional logs measured in a vertical well, and it uses the estimated slownesses of the assumed horizontal layers to model noise-mitigated sonic logs. By making use of geometric and physical constraints for noise reduction implicit in the inversion-based method, we obtain sonic logs that more accurately reflect the physical properties of rock formations penetrated by wells. Sonic logs are efficiently modeled by invoking axial sensitivity functions. First, we test the inversion-based method with synthetic sonic logs contaminated with noise. Estimated layer-by-layer slownesses agree with those of the original model within a standard deviation of [Formula: see text], while effectively reducing the numerical noise included in the input measurements. When bed-boundary locations are unknown, we perform the inversion-based method by assuming bed boundaries uniformly spaced at the same sampling interval of sonic logs; in this case, although the accuracy of the estimated layer slownesses decreases, the noise on sonic logs decreases. Then, we apply the method to sonic logs acquired in the North Sea and estimate angle reflectivity from the noise-mitigated logs. Results verify the reliability of the inversion-based method to reduce biases in the calculated angle reflectivity within a few minutes of central processing unit time.

Microwave Dielectric Properties of CCTO/PVA Composites

The CaCu3Ti4O12 (CCTO) ceramic powder was inserted in the polyvinyl alcohol (PVA) polymeric matrix, with an increasing weight fraction of the filler, to form a flexible and high dielectric constant composite at the GHz region. The structural characterization of the samples was performed using X‐ray diffraction and scanning electron microscopy (SEM). The complex permittivity was calculated by the small perturbation theory using two resonant cavities (2.7 GHz and 5.0 GHz). Several classical models (Maxwell Garnett, Lichtenecker, effective medium theory (EMT), and Yamada) were used to fit the real part of the complex permittivity of the composite as a function of the weight fraction of CCTO powder inserted in the PVA matrix. The best predictions for the dielectric behavior of these samples were obtained with the EMT and Yamada models.

Screening polyethylene oxide-based composite polymer electrolytes via combining effective medium theory and Halpin-Tsai model

Polyethylene oxide (PEO) based materials are promising candidates for the matrices in composite solid polymer electrolytes (CSPEs) for high-energy density lithium ion batteries. Experimental screening of high-performance CSPEs with high efficiency still appears to be challenging for the moment, due to the complications of the compositions involved. Here, we propose and test the joint application of effective medium theory (EMT) and Halpin-Tsai model that can predict with satisfactory accuracy the effects of the filler volume fractions and of the particle sizes on the conductivities and Young’s moduli of CSPEs. The application of this theoretical framework can be extended to other polymer based CSPEs and potentially enables us to build a CSPEs database for data mining to accelerate the screening process.

Calcium copper titanate/polyurethane composite films with high dielectric constant, low dielectric loss and super flexibility

Calcium copper titanate(CCTO)/polyurethane composite films with high dielectric constant, low dielectric loss and super flexibility were fabricated by incorporating CCTO ceramic powders into millable polyurethane elastomer (MPU) matrix using a rubber milling combined with hot compression molding method. The composite films show uniform microstructures and the dielectric constant is as high as 35.2 while the dielectric loss is only 0.041 when CCTO content reaches 40vol% at 100Hz and room temperature (RT). Moreover, it is important to note that this film has stable dielectric constant and dielectric loss in a relatively wide temperature range (from 0°C to 70°C), which is significantly import to the practice use of electronic devices based on CCTO composites. In addition, the flexibility of the film could be retained even when the CCTO content is up to 40vol% and the elongation at break of this composite film is as high as 159.1%. Theoretical analysis indicates that the experimental data are in good conformity to the effective medium theory (EMT) model with a derived n = 0.21, suggesting more close association of the dielectric constant with the CCTO filler size and shape.

Equivalence of effective medium and random resistor network models for disorder-induced unsaturating linear magnetoresistance

A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological random resistor network model constructs a grid of four terminal resistors, each with a varying random resistance. The effective medium theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the random resistor network is actually equivalent to the effective medium theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e., the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.

A Method for Quantitative 3D Mesoscale Analysis of Solid Oxide Fuel Cell Microstructures Using Xe-plasma Focused Ion Beam (PFIB) Coupled with SEM

Three-dimensional (3D) distributions of microstructural features in electrodes of solid oxide fuel cells (SOFCs) directly influence their electrochemical performance. Commercial grade SOFCs produced in cost-constrained environments can be expected to exhibit variations on the mesoscale (≈ hundreds of µm) of the microscale features (≈ tens of µm) that determine the local electrochemical activity. We are interested in quantitatively determining the mesoscale distributions of microscale properties in SOFC electrodes, especially quantifying the tails of distributions to establish correlations between such outliers and long-term performance. In this talk, we describe a new method that allows for the fast reconstruction of incredibly large volumes while maintaining a resolution on the order of tens of nm, allowing for fine-scale features to be accurately quantified. We use a Xe plasma focused ion beam (FIB) for slicing and a scanning electron microscope (SEM) for imaging. The pFIB allows for an increase in material removal rates by a factor of ≈ 100 compared to Ga ion FIBs, while the SEM resolution remains very high (herein ≈ 50nm), comparable to nano-CTs. In the same time as required for collecting Ga-FIB or nano-CT data sets, we collected a pFIB volume that is ≈ 70-80 times larger than attainable with Ga-FIB-SEM and ≈15-20 times larger than with nano-CT. From this data, we quantified the mesoscale distributions, containing both the mean and the variance, of key microscale features including volume fraction, average particle size, tortuosity, and triple phase boundary density. The commercial SOFC electrodes investigated were found to exhibit significant variations in the mesoscale distributions of their local microstructural features, which will be discussed. Importantly, these mesoscsale variations in microstructural features are expected to result in significant variations in electrochemical activity throughout the electrode. Using an effective medium theory model of polarization resistance, we quantified the distribution of microscale polarization resistance and mapped it spatially. Though the average value of polarization resistance is within range of expectation, the measoscale distribution of the microscale/local value of polarization resistance around the average indicates that several local areas are well outside the average, and potentially operating in regions expected to impact long-term cell performance.

Dielectric constant calculation based on mixture equations of binary composites at microwave frequency

Abstract The effective microwave dielectric constants of binary composites are examined through mixture equations in this paper. The ratios of dielectric constant of filler material to that of matrix material are studied from 0.77 to 24.55 and 0.21 to 9.53 in small and large volume fractions of filler material, respectively. The most adequate mixture equation for predicting the dielectric constants of binary composites is suggested. It was found that all mixture equations could give reasonably good predictions under similar dielectric constant between filler and matrix material situation and in the small volume fraction region. The effective medium theory model matched well for all volume fractions and a small amount secondary phase existence. Moreover, precision can be improved by the porosity corrected relative permittivity of composites.

Research on the equivalence between digital core and rock physics models

In this paper, we calculate the elastic modulus of 3D digital cores using the finite element method, systematically study the equivalence between the digital core model and various rock physics models, and carefully analyze the conditions of the equivalence relationships. The influences of the pore aspect ratio and consolidation coefficient on the equivalence relationships are also further refined. Theoretical analysis indicates that the finite element simulation based on the digital core is equivalent to the boundary theory and Gassmann model. For pure sandstones, effective medium theory models (SCA and DEM) and the digital core models are equivalent in cases when the pore aspect ratio is within a certain range, and dry frame models (Nur and Pride model) and the digital core model are equivalent in cases when the consolidation coefficient is a specific value. According to the equivalence relationships, the comparison of the elastic modulus results of the effective medium theory and digital rock physics is an effective approach for predicting the pore aspect ratio. Furthermore, the traditional digital core models with two components (pores and matrix) are extended to multiple minerals to more precisely characterize the features and mineral compositions of rocks in underground reservoirs. This paper studies the effects of shale content on the elastic modulus in shaly sandstones. When structural shale is present in the sandstone, the elastic modulus of the digital cores are in a reasonable agreement with the DEM model. However, when dispersed shale is present in the sandstone, the Hill model cannot describe the changes in the stiffness of the pore space precisely. Digital rock physics describes the rock features such as pore aspect ratio, consolidation coefficient and rock stiffness. Therefore, digital core technology can, to some extent, replace the theoretical rock physics models because the results are more accurate than those of the theoretical models.

A theoretical and numerical study on the gas-contributed thermal conductivity in aerogel

In this paper, a modified model for predicting the gaseous thermal conductivity in aerogel pores is proposed based on the kinetic theory of gases and the data from Direct Simulation Monte Carlo (DSMC) method. With the proposed modified model and the classical Effective Medium Theory (EMT) model, a gas-contributed thermal conductivity model which includes the equivalent gaseous thermal conductivity and the solid-gas coupling thermal conductivity is derived. The present gas-contributed model is validated by available experiment results for different types of aerogels. Comparisons between the present model and existing models show that the present gas-contributed model has a higher accuracy without complex calculations and assumptions.

Interfacial Polarity Modulation of KTa0.5Nb0.5O3 Nanoparticles and Its Effect on Dielectric Loss and Breakdown Strength of Poly(vinylidene fluoride) Nanocomposites with High Permittivity

The effects of the morphology, interface, and dielectric constant of inorganic fillers on the dielectric properties of nanocomposites were systemically studied in this paper. It is found that two kinds of KTa0.5Nb0.5O3 (KTN) nanoparticles, synthesized via solid-state reaction and hydrothermal method respectively, can bring different influences on the structure and electrical performance of the KTN/PVDF composites. This is caused by the OH groups on the surface of the H-KTN nanoparticles which were generated through the hydrothermal method. Theoretical models, including the Maxwell–Garnett model, logarithmic model, Jayasundere–Smith model, effective medium theory model, and Weibull distribution method, are employed to explain the dielectric behavior of the composite. Through the comparison between the experimental data and theoretical models, it is concluded that the geometric shape of fillers plays a more crucial role than the dielectric constant of fillers in enhancing the dielectric constant of KTN/PVDF...

Moth-Eye-Inspired Biophotonic Surfaces with Antireflective and Hydrophobic Characteristics.

In nature, in order to prevent attention from predators, the eyes of night-flying moths have evolutionarily developed an antireflective ability. The surfaces of their eyes are covered with a layer of a sub-wavelength structure that eliminates reflections of visible light. This layer allows the eyes of moths to escape detection in darkness, without reflections that could reveal the position of the moths to potential predators. In this study, we proposed a novel procedure for manufacturing a non-close-packed polystyrene (PS) nanosphere monolayer by combining the Langmuir-Blodgett (LB) deposition technique and oxygen plasma treatment. An antireflective structure was replicated from the sub-wavelength structure of moth eyes onto the surface of a glass substrate by nano-imprinting lithography; the structure also displayed hydrophobic properties. The Fresnel reflection of the replicated sub-wavelength structure is near the theoretical prediction from the effective medium theory model. The biomimetic moth-eye structure can be applied to solar cells, monitors, light-emitting diodes, and other optical devices in the future.

QUANTITATIVE ASSESSMENT OF FREE GAS BENEATH GAS HYDRATE STABILITY ZONE FROM PRESTACK SEISMIC DATA AND ROCK PHYSICS: A CASE OF HOLE NGHP01‐10A, KRISHNA‐GODAVARI BASIN, INDIA

AbstractThe distribution, saturation, and hydrate indicator of free gas beneath gas hydrate stability zone have been the difficulty in the research of gas hydrate. Amplitude versus offset (AVO) and rock physics can be used to quantitatively interpret free gas saturation. In this paper, seismic data, acquired at K‐G basin, India, are processed to preserve true amplitude information. Based on the logging data and horizon calibration, free gas saturation of NGHP01‐10A is assessed with effective medium theory and AVO modeling. It is found that free gas saturation is related to its distribution patterns. Assessments of free gas saturation in homogeneous and patchy distribution are 0.3%∼0.4% and 3%∼4%, respectively. The results show good agreement with the crossplot of Poisson's ratio which are calculated from the measurement at NGHP01‐10D. Free gas is further deduced to be homogeneous distribution on the base of dry frame Poisson's ratio with the saturation of 0.3%∼0.4%.

Dielectric Characteristics of UV‐Curable CaCu3Ti4O12 Composite Thick Film Capacitors on Cu Foils

Dielectric composite thick films containing a high dielectric constant CaCu3Ti4O12 (CCTO) filler in a UV‐cured polymer matrix were investigated as flexible planar capacitors on Cu foils. Dielectric performance depended on the volume fraction and size of CCTO particles dispersed in the cured polymer matrix. As a result, the thick films containing 33.3 vol.% CCTO with an average particle size of 0.47 μm exhibited a dielectric constant of ~80 and a dielectric loss of ~0.06 at 10 kHz. The effective medium theory model incorporating a morphology fitting parameter has been proven to be most close to the experimental values.

Largely enhanced thermal and electrical conductivity via constructing double percolated filler network in polypropylene/expanded graphite – Multi-wall carbon nanotubes ternary composites

In this study, we report a sharp increase of both thermal and electrical conductivity in polypropylene (PP) via formation of double percolated filler network with dense small-sized multi-wall carbon nanotubes (MWCNT) network located within loosened large-sized expanded graphite (EG) network. The electrical conductivity of PP/EG composites which levels off after the percolation threshold can be further enhanced by adding MWCNT and is increased two orders of magnitude as the content of MWCNT reaches to its threshold. Besides, the thermal conductivity of PP/EG-MWCNT increases by 38.5% compared to PP/EG and is much higher than PP/MWCNT. Furthermore, an excellent electromagnetic interference shielding effectiveness of ∼60 dB is obtained at the sample thickness of only 1.3 mm. Then, effective medium theory model is applied to analyze the mechanism for the largely enhanced thermal and electrical conductivity. It is suggested that formation of double percolated filler network, in which three types of connections exist between EG and EG, EG and MWCNT as well as MWCNT and MWCNT, could effectively reduce the interface thermal resistance. Our work is important and provides some new idea for the preparation of polymer composites with excellent thermal and electrical conductivity via constructing double percolated filler network.

A Review and Evaluation of Prediction Models of Gas Permeation for a Blended Flexible Packaging Film

Barrier properties of blended film, such as oxygen permeability, are a collective behaviour contributed by different resins. This study reviews 10 most widely used prediction models of gas permeation for two‐phase blended film along with their assumptions and the interconnection and similarities between these models. Two blended blown films, LDPE/EVOH and PET/PEN, were produced representing two different permeability ratios of matrix‐to‐disperse phase. Effective oxygen permeability of the blended films was predicted by the models and compared with measured values. Scanning electron microscopy (SEM) micrographs of both films were obtained to understand the morphology in relation to gas permeation. The Fricke model and the effective medium theory model are recommended in this study to predict effective permeability of a blended flexible packaging film. Copyright © 2016 John Wiley & Sons, Ltd.

Three dimensional printing of high dielectric capacitor using projection based stereolithography method

We report that efficient high dielectric polymer/ceramic composite materials can be optically printed into three-dimensional (3D) capacitor by the projection based stereolithography (SLA) method. Surface decoration of Ag on Pb(Zr,Ti)O3(PZT@Ag) particles were used as filler to enhance the dielectric permittivity. Polymer nanocomposites were fabricated by incorporating PZT@Ag particles into the photocurable polymer solutions, followed by exposure to the digitally controlled optical masks to generate 3D structures. The dielectric permittivity of Flex/PZT@Ag composite reaches as high as 120 at 100Hz with 18vol% filler, which is about 30 times higher than that of pure Flex. Furthermore, the dielectric loss is as low as 0.028 at 100Hz. The results are in good agreement with the effective medium theory (EMT) model. The calculated specific capacitance of our 3D printed capacitor is about 63Fg−1 at the current density of 0.5Ag−1. Cyclic voltammetry (CV) curves indicate 3D printed capacitors possess low resistance and ideal capacitive properties. These results not only provide a tool to fabricate capacitor with complex shapes but lay the groundwork for creating highly efficient polymer-based composites via 3D printing method for electronic applications.

Theoretical model of the equivalent elastic modulus of a cobblestone–soil matrix for TBM tunneling

Cobblestone–soil mixed ground is a composite comprising cobblestones surrounded by soil. It is typical mixed-face ground encountered during tunnel boring machine (TBM) tunneling, and it may result in cutter wear, jamming of the roller cutterhead, poor TBM performance and cost overruns. The present paper investigates the deformation problem of cobblestone–soil mixed-face ground during TBM excavation. The ground under study is composed of two components (soil matrix and cobblestones) usually firmly bonded together at the interface, and can be regarded as a continuum. Previous studies have proposed many theoretical models for a composite material with two components. Representative models include the parallel model, series model, and effective medium theory model. Nonetheless, these models are limited by their assumptions and preconditions. In the present study, under an assumption of uniform strain, analytical solutions were derived for the equivalent elastic modulus while the cobblestone is assumed to be perfectly spherical or ellipsoidal. Triaxial compression tests were carried out to validate the analytical solutions. The equivalent elastic modulus derived from the triaxial experiments and theoretical models matched rather closely. The analytical solutions are helpful in clarifying the deformation of such ground and enhancing TBM performance.

Validations of a Model to Estimate Thermal Conductivities of Ceramics

The Effective Medium Theory Model (EMTM) used in this work is based on the assumption that every phase of the matrix is embedded in a homogeneous medium with conductivity <i>k_eff</i> to be determined self-consistently. It is based on dilute spherical inclusions of one phase embedded in a matrix of a second phase. Several Samples of composite ceramics that are mechanically strong, relatively non-porous and anisotropic have been investigated. A comparison between the measured data and the results predicted by EMTM were made to validate the model for these ceramic samples. In particular, we investigate the effect of mineralogy (constituents) in ceramics and their spatial distribution profile to validate the homogeneity conditions of the model. Preliminary indicators of validation were used to check the bulk and surface homogeneities. This can be done either by roughly estimating Wiener bounds or by examining microscopically the surfaces of the samples. It turns out that the EMTM is a suitable one to estimate <i>k_eff</i> provided that the homogeneity conditions are satisfied.

Effective thermal conductivity prediction of foods using composition and temperature data

Thermal conductivity data are important for food process modelling and design. Where reliable thermal conductivity data are not available, they need to be predicted. The most accurate ‘first approximation’ methodology for predicting the isotropic thermal conductivity of foods based only on data for composition, initial freezing temperature and temperature dependent thermal conductivity of the major food components was sought. A key feature of the methodology was that no experimental measurements were to be required. A multi-step prediction procedure employing the Parallel, Levy and Effective Medium Theory models sequentially for the components other than ice and air, ice and then air respectively is recommended. It was found to provide the most accurate predictions over the range of foods considered (both frozen and unfrozen, porous and non-porous). The Co-Continuous model applied in a single step also provided prediction accuracy within ±20% (on average), except for the porous frozen foods considered. For greater accuracy more rigorous modelling approaches based on knowledge of the foods structure would be required.