Effective Medium Theory Model Research Articles

Distributions of local electrochemistry in heterogeneous microstructures of solid oxide fuel cells using high-performance computations

A high-throughput, high-performance computational approach is used to simulate local electrochemistry in three-dimensions of solid oxide fuel cell electrodes, with the aim of understanding distributions of performance values within microstructures. Simulations are carried out on 47 three-phase cathodes, whose lateral {vertical} dimensions are 22 {15} times their average particle size (0.46 μm). The 47 microstructures are spread across four distinct groups having different standard deviations in their particle size and/or local volume fraction distributions. The average performance simulated compares favorably to two accepted effective medium theory (EMT) models, but a significant discrepancy between the locally-resolved simulations and the EMT models arises from the Ohmic transport terms. This is borne out further by local electrochemical values, specifically distributions of local activation overpotentials and regions of extremely high current densities: values often connected with degradation. The impact of particle size and volume fraction distributions on the distribution of performance values–both within and between microstructural groups—is highlighted throughout. Results from this study indicate that high-performance simulations in a high-throughput, large-data workflow can elucidate performance characteristics that are not captured by continuum level models using EMT. Understanding of these detailed performance characteristics is expected to lead to more durable and reliable electrochemical cells.

Enhancing thermal conductivity of C/SiC composites containing heat transfer channels

In this study, CNTs/SiC micro-pillars at controlled content ratios were introduced into C/SiC composites as heat transfer channels to improve the thermal conductivity in the thickness direction. The thermal conductivities and bending strengths before and after heat treatment at 1650 °C were investigated and the results were discussed. The theoretical calculations and finite element analyses confirmed that CNTs/SiC micro-pillars successfully worked as heat transfer channels. The theoretical thermal conductivity calculated by effective medium theory (EMT) model was 19.25 W/m⋅k and agreed-well with the experimental value. The measured thermal conductivity was estimated to 20.69 W/m⋅k and improved to 22.36 W/m⋅k after heat treatment. The latter was 3.56-fold higher than that of traditional C/SiC and attributed to increased grain growth during heat treatment. The optimal bending strength before heat treatment was recorded as 324.5 ± 23.74 MPa due to microstructure evolution caused by CNTs. After heat treatment, the bending strength improved by 138 % with ductile fracture mode attributed to ordered layer structure of PyC interphase and complex phase composition of the composites. These features benefited the abundant propagation of cracks and energy consumption. In sum, introduction of heat transfer channels into C/SiC composites provided a new way to improve the thermal conductivity in thickness direction of ceramic matrix composites.

Thermal Conductivity of Gold–Phenylethanethiol (Au144PET60) Nanoarrays: A Molecular Dynamics Study

Solvated nanoarrays of Au144 nanoparticles capped with 60 phenylethanethiol (PET) moieties were studied using reverse nonequilibrium molecular dynamics (RNEMD) simulations. The thermal conductivities of the nanoarrays were computed for two chemically dissimilar solvents. These were compared to an effective medium theory (EMT) model based solely on bulk and interfacial properties and the volume fraction taken up by the particles. The interfacial thermal conductance for isolated particles was also estimated via RNEMD using individual solvated particles in nonperiodic geometries. A strong system-size dependence was found in bulk conductivity calculations, particularly in the polar solvent, dichloromethane, but was found to be unimportant in a second nonpolar solvent (toluene). However, the bulk conductivity of solvated nanoarrays also requires projection to infinite system size. The Au144PET60 particles were found to display a molten core at the temperatures used in this study. Our primary finding is that the volume fraction of the metal particles is the primary variable controlling the thermal conductivity of the nanoarrays and that simulated conductivities are predicted well by the EMT model.

Multiscale simulation of gas transport in mixed-matrix membranes with interfacial polymer rigidification

Abstract We investigate permeation in non-ideal mixed-matrix membranes (MMMs) having interfacial defects based on a multiscale simulation approach, involving sequential nanoscale and macroscale simulations. Our approach combines insight from equilibrium molecular dynamics (EMD) simulation of the transport in the individual phases, and in the interfacial region, with macroscopic simulation of the transport through solution of coupled 3-D partial differential equations (PDEs) via a finite-element method (FEM). Thus, unlike existing adaptations of classical effective medium theory (EMT), our approach avoids the empirical fitting of filler-polymer interfacial properties, such as interfacial thickness and permeability, against experimental permeation data. While the proposed multiscale simulation approach is general and applicable to any MMM system, it is illustrated in the context of single CO 2 and CH 4 permeation in two different polyimide-based MMMs; with one using MFI-type zeolite as filler phase and the other using carbon molecular sieves (CMS). For both systems, our nanoscale simulations reveal an interfacial region with rigidification of the polymer and reduced permeability at the polymer-adsorbent interface. Comparison of permeability predictions of classical EMT-based models considering interfacial rigidification, with our macroscale simulations, demonstrates the former to be best at low particle loadings. Further, our macroscale simulations reveal the existence of an optimum filler particle size, never discussed before, which maximizes the permeability in non-ideal MMMs; this arises from the competing effects of decrease in permeability and decrease of the relative interfacial resistance with increase of filler particle size. Moreover, the CO 2 / CH 4 perm-selectivity is found strongly sensitive to the interfacial resistance for both finite uniform and non-uniform particle size distributions, an effect not captured by existing EMT models and overlooked in prior fundamental approaches.

Quantitative Analysis of Multi-Scale Heterogeneities in Complex Electrode Microstructures

A semi-empirical model is developed to quantitatively characterize electrode heterogeneities over the micro- and mesoscales, specifically between the relationship of the mean-squared normalized variance in the volume fraction, , and the mean particle size normalized linear dimension, . The model was developed analyzing data from five large-volume physical reconstructions – collected using Xe-plasma focused ion beam with SEM (PFIB-SEM) – of several commercial cell electrodes and from unique sets of synthetic microstructures designed to have controlled distributions in particle size and local volume fractions. When comparing physical reconstructions from distinct regions of the same electrode, millimeter length scale heterogeneities are also observed, even in microstructures with limited mesoscale variability. While the model is developed using synthetic microstructures, it is used to quantify three different types of heterogeneities in the commercial cells. The potential origins are discussed with respect to variations in particle size distributions in feedstocks and to phase distributions related to fabrication processes; the potential performance impacts are discussed with respect to two effective medium theory models. The characterization and analytical methodologies and model presented can support the design and development of improved electrodes.

Synergistic enhancement of thermal conductivity for low dielectric constant boron nitride–polytetrafluoroethylene composites by adding small content of graphene nanosheets

Abstract Polymer composite with high thermal conductivity (TC) and low dielectric property has great applications in electronic packaging. Herein, we fabricated a series of boron nitride nanosheets–graphene nanosheets–polytetrafluoroethylene (BNNs–GNs–PTFE, BGP) composites, in which the GNs contents of composites were all constant at 1 wt%, via liquid mixing, followed by cold-pressing and sintering. The results demonstrated that the BGP composites possessed good crystallization, excellent thermal stability, high TC and low dielectric property. When BNNs–GNs content was 25 wt%, the BGP composite had a TC of 1.41 W m−1 K−1. The synergetic effect of BNNs and GNs on the enhancement of composite's TC was investigated with a modified effective medium theory (EMT) model. In addition, we found that the dielectric constant and dielectric loss of BGP composites remained at a low level. The study indicated that adding small content of GNs into BNNs–PTFE composite can significantly enhance the composite's TC, while maintaining its low dielectric constant.

Effect of frequency of microsecond pulsed electric field on orientation of boron nitride nanosheets and thermal conductivity of epoxy resin-based composites

Nanosecond pulsed electric fields over 200 kV/mm have been used for filler alignment in polymer-based thin film (120–250 μm) composites to improve their thermal conductivity, but little research has been performed on bulk composites because of the requirement of an extremely high nanosecond pulsed voltage. In this paper, a microsecond pulsed voltage with a pulse width of 1 μs and an electric field of only 11.76 kV/mm was adopted for the first time to prepare bulk composites of 1.7 mm. The effects of frequency on nanosheets’ orientation and the thermal conductivity of epoxy composites were studied. The orientation degree of BN nanosheets was determined based on cross-sectional scanning electron microscopy images and X-ray diffraction peaks. The orientation degree and thermal conductivity of epoxy composites increased with the increase of the frequency, but the increase rate was lower under higher frequencies. The thermal conductivity of composites containing 10 wt. % BN nanosheets prepared under 100 Hz was 0.588 W/mK, which was more than twice that of composites without an applied electric field. Additionally, an effective medium theory model was adopted for thermal conductivity modeling. In addition, thermogravimetric and differential scanning calorimetry analyses were performed to evaluate the thermal properties of the composites. The results showed that after BN orientation in epoxy resin, the composites had higher glass transition temperature and better thermal stability. Microsecond pulsed electric fields are promising for preparing bulk insulation composites with higher thermal conductivity.

A case study on the applicability of elastic velocity models to hydrate-bearing sediments

Acoustic properties play an important role in the identification of natural gas hydrate resources, the estimation of their potential yield and the evaluation of soil stabilisation during exploration. Physical properties, such as hydrate saturation, porosity and clay content, are dominant factors that affect the acoustic properties of sediments. When considering these properties, the modified Biot–Gassmann theory of Lee (BGTL), the effective-medium theory (EMT) and the Frenkel–Gassmann equation (FG) are adopted to show the characteristics of compressional and shear wave velocities due to variation of the physical properties of different sediments. The results show that hydrate saturation has the highest sensitivity in the three models, followed by the porosity and clay content. To evaluate the applicability of different models, the data from two case studies are compared – actual survey data from the site995 stations and 2L-38 logging. The results indicate that the BGTL and EMT models are more suitable for hydrate-bearing sediments with a hydrate saturation less than 10%, a clay content of 50–70% and a porosity of 60–70%, while the FG model is more suitable for hydrate-bearing sediments with a hydrate saturation of 30–70%, a clay content of 30–60% and a porosity of 30–50%.

Dielectric and piezoelectric properties of lead free BZT-BCT/PVDF flexible composites for electronic applications

In this study, a lead-free 0.50[Ba(Zr0.2Ti0.8)O3]0.50(Ba0.7Ca0.3)TiO3 (BZT-BCT) ferroelectric powder was prepared and used as a filler to fabricate 0–3 connectivity ceramic-polymer composites using polyvinylidene fluoride (PVDF) as the matrix in the development of flexible devices for electronic applications. Four composites with different weight fractions x(BZT-BCT)-(1−x)PVDF, where x = 35, 45, 50, and 65 wt%, were prepared by employing melt mixing and a hot-pressing method. X-ray diffraction analysis showed the presence of ceramic (functional reinforcements) and polymer (matrix) phases in the composite material. Scanning electron microscopy images confirmed uniform dispersion of the ceramic filler in the PVDF matrix. Dielectric, ferroelectric, and piezoelectric analyses were carried out on the composite samples, the results of which are discussed in detail. The composite with x = 65 wt% ceramic showed the highest dielectric constant (ε′) of 49 and a dielectric loss of ≤0.03 measured at a frequency of 1 kHz. In addition, the piezoelectric charge coefficient (d33) reached a maximum of 9 pC/N when measured at 100 Hz after 24 h of sample poling when measured at room temperature. The relaxor behaviors of the composites are the same as that of pure PVDF and the ferroelectric polarization response of the composites is significantly influenced by the incorporation of BZT-BCT filler particles within the PVDF matrix. The experiment data were fitted to the theoretical equations, and modified Kerner, Yamada, and effective medium theory models were found to be useful for predicting the dielectric constant of the composites.

The impact of polymer matrix blends on thermal and mechanical properties of boron nitride composites

ABSTRACTTo improve mechanical and thermal properties of a hexagonal boron nitride platelet filled polymer composites, maleic anhydride was studied as a coupling agent and compatibilizer. Injection molded blends of acrylonitrile butadiene styrene (ABS), high‐density polyethylene (HDPE), and maleic anhydride with boron nitride filler were tested for thermal conductivity and impact strength to determine whether adding maleic anhydride improved interfacial interactions between matrix and filler and between the polymers. Adding both HDPE and maleic anhydride to ABS as the matrix of the composite resulted in a 40% improvement in impact strength without a decrease in thermal conductivity when compared to an ABS matrix. The best combination of thermal conductivity and impact strength was using pure HDPE as the matrix material. The effective medium theory model is used to help explain how strong filler alignment helps achieve high thermal conductivity, greater than 5 W/m K for 60 wt % boron nitride. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 137, 48661.

A double mixing process to greatly enhance thermal conductivity of graphene filled polyamide 6 composites

Tremendous investigations have been recently conducted to increase the thermal conductivity (TC) of nanofiller filled thermoplastic composites. However, the agglomeration of nanofillers limits their loading and is a bottleneck to further increase the TC of composites. In this work, a preparation technique combining the benefits of both solution mixing and melt blending is proposed, with which high loading and good dispersion of graphene sheets (GSs) filled polyamide 6 (PA6) matrix composites are achieved. Noteworthily, the through-plane TC of the composites reaches 3.55 W m−1 K−1 with 20 wt% GSs, corresponding to a TC enhancement of 1167% compared to pure PA6. The excellent performance can be attributed to high loading and uniform dispersion of GSs, which facilitate the formation of thermally conductive network for efficient heat transfer. An effective medium theory model by taking the filler-to-matrix and filler-to-filler interfacial effects into consideration is also proposed to perceive the behind mechanism. The theoretical calculation agrees well with our experimental results. Moreover, we find the Young’s modulus of the composite increases significantly and the tensile strength nearly remains unchanged even at a GSs filler loading of 20 wt%. The results provide an effective and facile route for developing low-cost and highly conductive thermoplastic composites.

High thermal conductive poly(vinylidene fluoride)-based composites with well-dispersed carbon nanotubes/graphene three-dimensional network structure via reduced interfacial thermal resistance

Polymeric materials exhibit superior advantages, while the low thermal conductivity greatly limited their applications in heat exchangers. In this study, a high thermal conductive poly(vinylidene fluoride) (PVDF) composite was prepared through constructing a three-dimensional network conductive structure with modified multi-wall carbon nanotubes (s-MWCNTs) and graphene (GE) in PVDF matrix. The thermal conductivity was enhanced by 711.1% in s-MWCNTs/GE/PVDF composite compared to that of PVDF. The results revealed that s-MWCNTs could not only effectively inhibit the stacking between GE lamellars and promote the formation of a well-dispersed three-dimensional s-MWCNTs/GE network structure, but also largely increase the interfacial compatibility between hybrid fillers and matrix. Above results were verified via a classic Effective Medium Theory model, confirming the significantly improved dispersibility and greatly reduced interfacial thermal resistance of composites. The formation of denser network structure for heat conduction was demonstrated and the mechanism for enhanced thermal conductivity was then presented. This work highlights an effective strategy to achieve excellent thermal conductive polymeric materials, which may eliminate the barriers for polymeric materials in applying in heat exchange fields.

A perspective on effective medium models of thermal conductivity in (ultra) nanocrystalline diamond films

Thermal conductivity of nanocrystalline and ultra-nanocrystalline films is analyzed with effective medium theory (EMT) models. The existing EMT models use the spherical inclusion approximation. Although this approximation works quite well it is inconsistent, mostly with respect to the maximal packing of 74{\%}, which may be unrealistic for polycrystalline films. To check the consistency of these models we devise an EMT model with arbitrarily shaped inclusions. We pick the EMT model with cubic inclusions and we compare its results with the results of the EMT model with spherical inclusions. It is found a very good agreement between both calculations. This agreement is explained by general geometrical arguments. We further employ these models to analyze thermal conductivity of nanocrystalline and ultra-nanocrystalline diamond films. It is noticed that the effective conductivity is strongly affected not only by the boundary Kapitza resistance but also by intra-grain scattering for grain sizes below 100 nm. Generally, both intra-grain conductivity and Kapitza resistance increase with grain size. However, the effect of Kapitza resistance increase is negligible due to the geometrical factor accompanying Kapitza resistance contribution to the effective conductivity.

Clustering effect on permeability spectra of magneto-dielectric composites with conductive magnetic inclusions

Magneto-dielectric composites, promising candidate materials for next-generation microwave communication, require high permeability and low loss, which are closely related to the particle size of the magnetic fillers. However, clustering occurs when particles physically or electrically touch each other, resulting in effective particle clusters that are much larger than the individual particle size. In this paper, we extend the effective medium theory (EMT) to include the clustering effect, which describes a more accurate prediction of the effective permeability of magneto-dielectric composites over wide ranges of both particle concentration and frequency. A Monte Carlo simulation is applied to model the agglomeration of magnetic particles suspended within a polymeric matrix. The extended formula is experimentally verified by the measurement of constitutive parameters, for iron/paraffin composites with various filler concentrations, over the frequency range from 1 MHz to 1 GHz. Considering the clustering effect, the proposed EMT model corrects the overestimation of the traditional EMT models, especially near the percolation threshold where the cluster size grows comparable to the skin depth at a given frequency.

Improved interfacial properties for largely enhanced thermal conductivity of poly(vinylidene fluoride)-based nanocomposites via functionalized multi-wall carbon nanotubes

Interfacial properties between fillers and polymer matrix are crucial for the enhanced thermal conductivity of composites. Considering that vinyl-containing groups can be compatible with poly(vinylidene fluoride) (PVDF) matrix, triethoxyvinylsilane (YDH-151) functionalized multi-wall carbon nanotubes (s-MWCNTs) were prepared and blended into PVDF to achieve high thermal conductive s-MWCNTs/PVDF nanocomposites. Functionalized s-MWCNTs not only showed better dispersion, but also significantly increased the interfacial compatibility with PVDF, contributing to the largely enhanced thermal conductivity. A thermal conductivity of 1.552 W/(m·K) was achieved in s-MWCNTs/PVDF composite with 10 wt% s-MWCNTs loading, about 9 times in comparison to that of pure PVDF matrix, which was much higher than that of the non-functionalized MWCNTs/PVDF composite (0.478 W/(m·K)) under the same loading weight. The enhanced thermal conductivity was verified by both theorical and experimental results. A classic Effective Medium Theory model proved that YDH-151 functionalization on MWCNTs significantly improved their dispersibility in PVDF matrix, and more importantly reduced the interfacial thermal resistance of composite, which was 68% lower than that of original MWCNTs/PVDF composite. Experimental rheological measurement confirmed the improved interfacial properties greatly promoted the formation of denser MWCNTs network structure in nanocomposites. This work highlights an effective strategy for realizing excellent thermal conductive polymeric composites and provides useful information to further reveal the mechanism of thermal conductivity.

Development and test of concentration scaled demagnetization in effective media theories of magnetic composites

Three effective medium theories (Maxwell-Garnett Theory, MGT; Bruggeman Effective Medium Theory, BEMT; and Coherent Model Approximation, CMA) are applied to predict magnetic susceptibility of polymer-magnetic particle composites and composite resonant frequency. Predictions are compared to the measurement of multi-crystalline magnetic particulate-polymer composites. Particulates had aspect ratios near unity; bulk low frequency susceptibilities ranged from 27 to 1000 s and particle volume fractions were between 5% and 100%. Emphasis was placed on CMA and BEMT. BEMT was selected for incorporation of a scaling function relating demagnetization with particulate concentration. The scaled model is scaled effective medium theory (ScEMT). Percolation theory and micromagnetic computations were applied to guide the choice of scaling function parameters. Experimental support of scale model physics was taken from measurements of magnetic sphere clustering in two dimensions. Scaling function constants and power laws w...

PVDF composites with spherical polymer-derived SiCN ceramic particles have significantly enhanced low-frequency dielectric constants

We report a novel functional hybrid film fabricated by using polysilazane-derived SiCN ceramics as fillers and polyvinylidene fluoride (PVDF) as the matrix. Regular spherical-shaped and amorphous SiCN ceramic powders were fabricated via a facile solvothermal method combined with a polymer-derived ceramic (PDC) process. The dielectric properties of the SiCN/PVDF composites were investigated by broadband dielectric spectroscopy from 0.1 Hz to 106 Hz. The composites showed significantly enhanced low-frequency dielectric constants. When the SiCN loading content reached 40 vol%, the dielectric constant of the composites was approximately 360 at 0.1 Hz, which is 20 times the value of pure PVDF (18). The dielectric constant of the composites at 0.1 Hz fit the effective medium theory (EMT) model well. The results suggest that the SiCN/PVDF composites are promising dielectric materials and have potential use in electrical applications.

A semi‐empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination‐number and Poisson‐ratio

ABSTRACTThe effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over‐predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non‐linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three‐step modified grain contact theory model to a two‐step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.

On the piezoresistive behavior of carbon fibers - Cantilever-based testing method and Maxwell-Garnett effective medium theory modeling

A good understanding of the piezoresistive behavior of carbon fiber is highly valuable in studying the processing-structure-property relationship of this very important engineering material. Up-to-date, there is still a lack of agreement on the physical origin of the unique modulus-dependent piezoresistivity for carbon fibers. In the present work, an experimental and theoretical modeling combined approach was taken to attack this long outstanding issue. A cantilever testing method was developed which allows for the evaluation of the piezoresistive behavior of a single carbon fiber filament under axial tension and compression mode. It was found that the tensile and compressive piezoresistive behavior showed antisymmetric characteristics. This supports the concept that the orientation of the basic structural units (BSUs) is responsible for the piezoresistivity of carbon fibers. Such an argument was further augmented by theoretical modeling of the carbon fiber piezoresistivity based on a Maxwell Garnett theory approach. The new piezoresistivity model identifies the critical role of the compound effect of the BSU orientation and its volume fraction in dictating the piezoresistive behavior of carbon fibers. With consideration of this compound effect, the modulus-dependent piezoresistivity data of carbon fibers reported in the past few decades can now be well explained.

Low dielectric lossBST/PTFEcomposites for microwave applications

AbstractBa0.3Sr0.475Ce0.03La0.12Ti0.997Mn0.003O3/Polytetrafluoroethylene (PTFE) composites were prepared using powder processing technique. The effects of the ceramic filler volume fraction and the coupling agent on the phase composition, microstructure, dielectric and thermal properties of the composites were investigated in this paper. The ceramic filler dispersion in thePTFEmatrix, thus the dielectric loss, permittivity, and dimensional thermal stability of the composite was considerably improved by the modification ofBSTfiller surface using phenyl trimethoxy silane (PTMS) coupling agent. Variation of the dielectric permittivity of the composite with composition was well fitted by the effective medium theory (EMT) model in the experimental compositional range. The obtained silane‐treated composite with 0.5 VfBSTexhibits extremely low dielectric loss:εr = 16, tanδ = 5.4 × 10−4@1MHz and 5.16 ± 0.6 × 10−3@ 10GHz. TheCTEof the composites was reduced to 43 ppm/°C.