Self-consistent Effective Medium Theory Research Articles

Understanding the electrical transports of p-type polycrystalline SnSe with effective medium theory

SnSe crystal is one of the most potential thermoelectric materials due to its excellent transport properties. The electrical conductivity of p-type SnSe crystal gradually decreases with increasing temperature, while that of the polycrystalline sample shows a completely different trend. We revealed that below 400 K, the existence of plentiful grain boundaries dominates the carrier scattering and determines the electrical transport of p-type polycrystalline SnSe, while at high temperatures, from 400 to 800 K, the electrical transport and conductivity curve still requires a clear understanding. In this study, by conducting the high-temperature synchrotron radiation x-ray diffraction (SR-XRD) measurements and refining the patterns, we obtained the phase fractions of Pnma and Cmcm phases in this temperature range. Using the derived single-phase theoretical electrical conductivity, combined with the self-consistent effective medium theory, the electrical conductivity of p-type polycrystalline SnSe between 400 and 800 K was simulated. This study provides a perspective and simulation method to understand the electrical transport of p-type polycrystalline SnSe.

Effect of magnetic-field-induced restructuring on the elastic properties of magnetoactive elastomers

Composite materials where magnetic micrometer-sized particles are embedded into a compliant polymer matrix are known as magnetorheological (or magnetoactive) elastomers (MAEs). They are distinguished by huge variations in their physical properties, when in a magnetic field, which is commonly attributed to the restructuring of the filler. The process of the magnetic-field-induced restructuring in a magnetorheological elastomer is interpreted as progression towards percolation. Such a physical model was previously used to explain the dependence of the magnetic permeability and dielectric permittivity of MAEs on the magnetic field strength. Based on this hypothesis, the magnetorheological effect in MAEs is considered theoretically. The theoretical approach is built upon a self-consistent effective-medium theory for the elastic properties, extended to the variable (field dependent) percolation threshold. The proposed model allows one to describe the large variations (over several orders of magnitude) of the effective elastic moduli of these composite materials, known as the giant magnetorheological (MR) and field-stiffening effects. The existence of a giant magnetic Poisson effect is predicted. The relation of the proposed model to the existing theories of the MR effect in MAEs is discussed. The results can be useful for applications of MAEs in magnetic-field-controlled vibration dampers and isolators.

Modeling large permittivity of poly(vinylidenefluoride-co-trifluoroethylene) and nanospring single-walled carbon nanotube-polyvinylpyrrolidone nanocomposites

Highly dispersible nanospring single-walled carbon nanotubes (NS-CNTs) were incorporated in a P(VDF-TrFE) copolymer with up to 15 wt.% of nanofiller. The relative dielectric constant (K) of the polymer nanocomposite at 1 kHz was greatly enhanced from 12.7 to 62.5 at 11 wt.% of NS-CNTs, corresponding to a 492% increase over that of pristine P(VDF-TrFE) with only a small dielectric loss tangent (D) of 0.1. Based on two theoretical models, the Bruggeman equation and self-consistent effective medium theory (SC-EMT), experimental permittivity data for the P(VDF-TrFE) and NS-CNTs nanocomposites were simulated to estimate the dielectric constant of the NS-CNTs while changing both the shape of the nanofillers and the volume fraction of the interface when increasing the number of NS-CNTs in piled layers of P(VDF-TrFE). The number of NS-CNTs layers was counted from HR-TEM images to calculate the interfacial volume fraction, and used to infer the Eshelby tensor of the NS-CNTs in the SC-EMT model. The experimental dielectric constants of the composite films fit the Bruggeman equation and SC-EMT theory well for dielectric constants k=240–360, showing that the NS-CNTs nanofillers may be considered electrically semiconductive.

BC/rGO conductive nanocomposite aerogel as a strain sensor

In this work, bacterial cellulose (BC)/reduced graphene oxide (rGO) as a new class of electrical conductive nanocomposite aerogels were in-situ synthesized and dried by the supercritical CO2 (ScCO2) drying method. A modification has been performed on the self-consistent effective medium theory to predict overall electrical conductivity of nanocomposite aerogels. It was observed that the porosity had a distinct effect on the overall electrical conductivity of nanocomposite aerogel beneath percolation threshold, but had no effect beyond it. The latter observation was attributed to the formation of continuous pathway associated with electron tunneling effect, beyond percolation threshold. The results also indicated that in the presence of rGO, the density, specific surface area and Young's modulus of nanocomposite aerogel increased up to 0.025 g/cm3, 252 m2/g and 2020 MPa, respectively. Also, the gauge factor of 19 obtained for BC/rGO nanocomposite aerogel indicated the potency of fabricated nanocomposite aerogel as a strain sensor.

Transport properties of multigrained nanocomposites with imperfect interfaces

Multigrained or polycrystalline composite materials have attracted a considerable attention due to their potential applications as advanced materials with outstanding thermal, mechanical, and electromagnetic properties. When the grains' morphology is displayed at the nanoscopic scale, the presence of imperfect interfaces plays a central role in determining the effective transport properties. Therefore, we develop here a self-consistent effective medium theory able to evaluate the influence of real contacts between the different phases of multigrained composite materials. This approach takes into account the classical interface schemes that have been introduced in literature, namely, the low and the high conducting interface models. The theoretical results have been compared with numerical and experimental data concerning the thermal conductivity of (1−x)Si:xGe mixtures and the electrical conductivity of (1−x)Li2O:xB2O3 composites.

Saturation effects on the joint elastic–dielectric properties of carbonates

We used a common microstructural model to investigate the cross-property relations between elastic wave velocities and dielectric permittivity in carbonate rocks. A unified model based on validated self-consistent effective medium theory was used to quantify the effects of porosity and water saturation on both elastic properties (compressional and shear wave velocities) and electromagnetic properties (dielectric permittivity). The results of the forward models are presented as a series of cross-plots covering a wide range of porosities and water saturations and for microstructures that correspond to different predominant aspect ratios. It was found that dielectric permittivity correlated approximately linearly with elastic wave velocity at each saturation stage, with slopes varying gradually from positive at low saturation conditions to negative at higher saturations. The differing sensitivities of the elastic and dielectric rock properties to changes in porosity, pore morphology and water saturation can be used to reduce uncertainty in subsurface fluid saturation estimation when co-located sonic and dielectric surveys are available. The joint approach is useful for cross-validation of rock physics models for analysing pore structure and saturation effects on elastic and dielectric responses.

Dielectric behaviors of PHBHHx–BaTiO 3 multifunctional composite films

Multifunctional polymeric composites were investigated for potential use in high energy storage capacitors and tissue engineering. The polymeric composites were fabricated by employing biodegradable polyester, poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx), as the matrix. Ferroelectric BaTiO 3 ceramic powders were added to the composites as fillers. The dielectric spectroscopy of the composites was measured over a wide frequency range (10 0–10 7 Hz) from −100 to 60 °C. The composition dependent dielectric behavior was modeled by a self-consistent effective medium theory. A percolation threshold of 0.367 was observed in the composites. The glass transition relaxation of the composite was also discussed by comparing the popular Vögel–Fulcher–Tammann law with a new glass model. The composites show attractive ferroelectricity and piezoelectricity for biomedical applications.

The effective dielectric constant of plasmas — A mean field theory built from the electromagnetic ionic T-matrix

This work aims to obtain the effective dielectric constant tensor of a warm plasma in the spirit of the derivation of a mixing law. The medium is made of non point-like ions immersed in an electron gas with usual conditions relating the various lengths which define the problem. In this paper the ion dielectric constants are taken from their RPA responses as developed in a previous paper [1]. Furthermore the treatment of the screening effects is made through a mathematical redefinition of the initial problem as proposed in Ref. [1]. Here the complete calculation of the T-matrix describing the scattering of an electromagnetic wave on an isolated ion immersed in an “effective medium” is given. It is used for building , in the spirit of a mixing law, a self-consistent effective medium theory for the plasma dielectric tensor. We then extend the results obtained in Ref. [1] to higher orders in ion or dielectric inclusion densities. The techniques presented are generic and can be used in areas such as elasticity, thermoelasticity, and piezoelectricity.

Effects of sand aggregate on ultrasonic attenuation in cement-based materials

Ultrasonic wave attenuation measurements have been successfully used to characterize the microstructure and mechanical properties of inhomogeneous materials; these ultrasonic techniques have the potential to provide for the in-situ characterization of microstructure changes in cement-based materials due to damage. Recent research has applied acoustic scattering models to quantitatively predict ultrasonic attenuation for evaluating the air void content in hardened cement paste. The objective of the current research is to investigate the influence of sand aggregate on the ultrasonic attenuation as a first step towards a full simulation of more realistic microstructures in real concrete. Hardened cement paste samples containing sand aggregate of varying volume fractions are considered. The research employs an independent scattering model and a self-consistent effective medium theory to predict the scattering-induced attenuation of longitudinal ultrasonic waves by the sand inclusions distributed in the cement paste matrix. The predicted attenuation coefficients are compared with measured ones. It is observed that at low volume fractions, both models provide a good estimate of the total attenuation in the specimens. These results indicate that it is possible to use a physics-based model to quantify the effect of sand aggregate on ultrasonic attenuation.

On the influence of spatial correlations on sound propagation in concentrated solutions of rigid particles

In a previous paper [J. Acoust. Soc. Am. 121, 3386-3387 (2007)], a self-consistent effective medium theory has been used to account for hydrodynamic interactions between neighboring rigid particles, which considerably affect the sound propagation in concentrated solutions. However, spatial correlations were completely left out in this model. They correspond to the fact that the presence of one particle at a given position locally affects the location of the other ones. In the present work, the importance of such correlations is demonstrated within a certain frequency range and particle concentration. For that purpose, spatial correlations are integrated in our two-phase formulation by using a closure scheme similar to the one introduced by Spelt et al. [''Attenuation of sound in concentrated suspensions theory and experiments," J. Fluid Mech. 430, 51-86 (2001)]. Then, the effect is shown through a careful comparison of the results obtained with this model, the ones obtained with different self-consistent approximations and the experiments performed by Hipp et al. ["Acoustical characterization of concentrated suspensions and emulsions. 2. Experimental validation," Langmuir, 18, 391-404 (2002)]. With the present formulation, an excellent agreement is reached for all frequencies (within the limit of the long wavelength regime) and for concentrations up to 30% without any adjustable parameter.

Floppy Modes and Nonaffine Deformations in Random Fiber Networks

We study the elasticity of random fiber networks. Starting from a microscopic picture of the nonaffine deformation fields, we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory. By relating nonaffinity to the low-energy excitations of the network ("floppy modes"), we achieve a detailed characterization of the nonaffine deformations present in fibrous networks.

Elastic Constants Relaxation in Disordered Heterogeneous Systems

Using self-consistent effective-medium theory, we studied the complex elastic compliances of conducting disordered heterogeneous piezoelectric-polymer systems. The considered system is a random mixture of piezoelectric spheroids and polymer ones with the same orientation. The proximate cause of the effective elastic constants frequency dependencies was considered. The nature of the obtained spectra was analyzed.

Traversal times for random walks on small-world networks

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate that is different from the rate for steps across small-world connections. When f>>F, the mean time to traverse the network exhibits a transition associated with percolation of the random graph (i.e., small-world) part of the network, and a collapse of the data onto a universal curve. This transition was not observed in earlier studies in which equal transition rates were assumed for all allowed steps. We develop a simple self-consistent effective-medium theory and show that it gives a quantitatively correct description of the traversal time in all parameter regimes except the immediate neighborhood of the transition, as is characteristic of most effective-medium theories.

Binary upscaling—the role of connectivity and a new formula

Although recognized as important, measures of connectivity (i.e. the existence of high-conductivity paths that increase flow and allow for early solute arrival) have not yet been incorporated into methods for upscaling hydraulic conductivities of porous media. We present and evaluate a binary upscaling formula that utilizes connectivity information. The upscaled hydraulic conductivity ( K) of binary media is determined as a function of the proportions and conductivities of the two materials, the geometry of the inclusions, and the mean distance between them. The use of a phase interchange theorem renders the formula equally applicable to two-dimensional media with inclusions of low K and high K as compared with the matrix. The new upscaling formula is tested on two-dimensional binary random fields spanning a broad range of spatial correlation structures and conductivity contrasts. The computed effective conductivities are compared to what is obtained using self-consistent effective medium theory, the coated ellipsoids approximation, and to a streamline approach. It is shown that, although simple, the proposed formula performs better than available methods for binary upscaling. The use of connectivity information leads to significantly improved behavior close to the percolation threshold. The proposed upscaling formula depends exclusively on parameters that are obtainable from field investigations.

Theory of intergranular magnetoresistance in nanometric manganites

We present a self-consistent effective medium theory for the magnetotransport in nanometric manganites on the basis of the bond-disordered resistor network. The transport process here is assumed to be controlled by both the charging energies of grains and the spin-polarized tunneling through grain boundaries. The effects of network and band-bending at the grain boundaries on the magnetotransport are investigated. Our results are compared with the experiments on nanometric ${\mathrm{La}}_{2∕3}{\mathrm{Sr}}_{1∕3}\mathrm{Mn}{\mathrm{O}}_{3}$ and ${\mathrm{La}}_{2∕3}{\mathrm{Ca}}_{1∕3}\mathrm{Mn}{\mathrm{O}}_{3}$; good agreements are found.

Self-consistent effective-medium approximation for strongly nonlinear media

A self-consistent effective-medium theory is proposed for random dielectric composites of arbitrary nonlinear constitutive law. It is based on a Gaussian approximation for the probability distributions of the electric field in each component, and on second-order Taylor expansions with an integral remainder of the local energies. The effective energy is exact to second order in contrast. With power-law media with constitutive relation $\mathbf{D}=\ensuremath{\chi}{E}^{\ensuremath{\gamma}\ensuremath{-}1}\mathbf{E},$ the critical exponents are $s=t=(\ensuremath{\gamma}+1)/2.$ The theory reduces to Bruggeman's in the linear case $\ensuremath{\gamma}=1,$ and its percolation threshold is independent of the nonlinearity.

A new theoretical description for anomalous birefringence of phase-separated glasses

Theoretical relationships between anomalous birefringence and microstructure of phase-separated glasses are proposed based on light scattering by particles and self-consistent effective-medium theory. A phase-separated and stretched glass generally has positive anomalous birefringence because the positive birefringence produced by form anisotropy of the secondary phase particles is larger than the negative birefringence produced by the distribution anisotropy of the particles. A postpulling heat-treated glass has negative birefringence because the form anisotropy decays and the distribution anisotropy remains. The magnitude of the anomalous birefringence increasesin particle size, particle size distribution variance, volume fraction of secondary phase, and uniaxial load. Results obtained by the theoretical model are consistent with available experimental results.

Energetics of icosahedral phase stability in metallic alloys.

Total-energy calculations based on self-consistent effective-medium theory are used to investigate icosahedral phase stability in aluminum--transition-metal binary alloys. We identify the mechanism of cohesion and explicate trends observed in diffraction experiments.

CONDUCTION THEORY OF IONIC CONDUCTOR CONTAINING DISPERSED SECOND PHASE

In this paper, an improved and simple self-consistent effective-medium theory is developed. The effect of dispersed second phase particle on the ionic conduction of ionic conductors is discussed by the theory. It is found that the theoretical result is consistent with experiments. The theory can perdict the effect of microscopic feature of the material on the macroscopic ionic conduction.

Electronic absorption of Frenkel excitons in topologically disordered systems

A self-consistent effective medium theory of the electronic absorption spectra of tightly bound dipolar excitons in simple fluids is developed within the adiabatic picture. The theoretical approach is based on the isomorphism between the path-integral formulation of quantum theory and classical statistical mechanics and is an extension of previous work [D. Chandler, K. S. Schweizer, and P. G. Wolynes, Phys. Rev. Lett. 49, 1100 (1982)]. The consequences of fluid structural disorder on resonant excitation transfer and the statistical fluctuations of single molecule energy levels are simultaneously treated. Detailed numerical calculations are performed to establish the dependence of the absorption spectrum on fluid density, short range order, and the relative magnitude of the resonant transfer vs the single site disorder. The density dependence of the spectral features are found to be a sensitive function of fluid structure and the relative strength of the localizing vs the delocalizing interactions. By comparing the liquid state results with the corresponding crystalline solid behavior, the consequences of topological disorder on the exciton spectrum are identified. The relevance of the theoretical predictions to spectroscopic probes of exciton delocalization in molecular liquids and glasses is discussed.