General Effective Media Model Research Articles

Structure-property relationships in the electrical conductivity of multilayer graphene sheet/epoxy nanocomposites

The relationship between the physicochemical properties of multilayer graphene sheets (GSs), their resulting state of dispersion, and the effective electrical conductivity of GS/epoxy nanocomposites is investigated. To construct such relationship, four types of GSs with dissimilar properties were physicochemically, structurally, and morphologically characterized, and correlated with the direct current and alternating current (AC) electrical responses of their polymeric nanocomposites. It was found that the most influential parameters that affect the electrical conductivity of the nanocomposites are the size and density of agglomerates formed at the mesoscale. Both parameters, in turn, are governed by the physicochemical properties of the individual GSs. At the nanostructure level, the lateral size of the GS arises as the most influential parameter, with larger GSs yielding higher conductivities and lower percolation thresholds. The carbon/oxygen ratio of the GSs also showed moderate influence. The nanocomposites showed a resistive (R)-capacitive (C) electrical response in AC, which fits to a two-element parallel RC model. Both, the power law and general effective media (GEM) models predict similar percolation thresholds, but the GEM model is more general and adequately reproduces the whole electrical curve for all filler concentrations.

Effective hydraulic conductivity of stony soils: General effective medium theory

Despite a longstanding interest in understanding the effects of rock fragments on soil hydraulic properties, physically-based models to describe the effective hydraulic conductivity of stony soils are still rare. The conductivity of stony soils is mostly described by simple scaling approaches, assuming impermeable rock fragments. We present a model based on the general effective medium (GEM) theory to calculate the effective hydraulic conductivity of stony soils. The model accounts for the volumetric content, shape, and orientation of rock fragments in the main direction of water flow. Rock fragments can either be permeable or impermeable in the model which allows to calculate the effective unsaturated hydraulic conductivity curve of stony soils over the full range of soil matric potentials. Existing models assume rock fragments to be isolated and their application is therefore limited to low to moderately stony soils. In GEM model interaction between rock fragments is allowed, which makes it applicable in stony soils with high contents of rock fragments. The mathematical simplicity of the model makes it suitable for practical applications and provides a strong theoretical basis for improving predictions of flow and transport in hydrological models applied in forested and agricultural watersheds and mountainous areas.

Electrical properties of extruded milled carbon fibre and polypropylene

A milled carbon fibre and polypropylene polymer composite at high filler loading was developed to produce conductive polymer composites for high conductive applications. Current research of conductive polymer composite material has reported about in-plane conductivity that was often higher than through-plane conductivity, which contradicted with the target of applications that required higher electrical conductivity in the through-plane direction. Therefore, electrical conductivity in parallel and transverse to extrusion directions were investigated. The general-effective media and modified fibre contact model were adapted to predict the electrical conductivity of the composite material. The experimental conductivity data of polypropylene/milled carbon fibre composites for transverse and parallel directions were not correlated with the general-effective media model with 2.009 and 0.663 S/cm, respectively, at the highest filler loading of 80 wt.%. This disagreement was due to various critical exponential, t values (2–3.25) that were obtained in this study. However, the modified fibre contact model seemed to have good agreement with the experimental data in the parallel to extrusion direction. This model was unable to predict electrical conductivity in the transverse direction due to lack of orientation occurring in that direction. The electrical conductivity increased as the filler loading increased as explained in percolation theory. Predicting the electrical conductivity of conductive polymer composites material is still in the preliminary stages where the researcher often obtains fluctuating agreement with the experimental values. Thus, contact between filler and orientation is considered as the main factor that influences the electrical conductivity and mechanical strength of the conductive polymer composites material.

Chemical-Mechanical Coupling Determines the Stability of Self-Supported Oxygen Ion Conducting Membranes

Introduction Ultrathin, self-supported oxide membranes are an emerging experimental platform to explore the limits of dimensionality reduction, probe the effects of chemically induced strain, and test proof-of-concept electrochemical devices.1,2 Integrating oxygen ion conducting (Y2O3)y(ZrO2)1-y (YDZ) electrolyte membranes into thin film solid oxide fuel cells (TF-SOFCs) has led to encouraging power densities of over 1 W/cm2 at relatively low temperatures of 500 °C. YDZ does not have the highest ionic conductivity in this temperature range. (Gd2O3)z(CeO2)1-z (GDC) exhibits a conductivity nearly an order of magnitude higher, though its electrolytic domain is much narrower, which affects both its electronic and mechanical properties.3,4 Since membranes integrated as electrolytes for TF-SOFCs must span an oxygen partial pressure range of ~1020atmospheres, the mechanical effects of chemically induced non-stoichiometry can be severe. Here, we will discuss a case study of archetypical ionic conductors, YSZ and GDC, integrated as membranes for self-supported electrolytes in TF-SOFCs. We introduce experimental methods to overcome the aforementioned challenges and present our resulting findings. Experimental YDZ and GDC thin films were grown by radio frequency sputtering in an Ar environment from stoichiometric ceramic targets. Self-supported membrane structures were fabricated using conventional semi-conductor processing techniques on low-stress Si3/N4 coated Si wafers. Additional detail on processing details of such structures can be found elsewhere.2 Solid-solution YDZ-GDC alloys were created by co-sputtering both materials simultaneously at a constant rate. Compositionally graded YDZ-GDC films were fabricated by co-sputtering both materials at a time-dependent rate, which translated into a varying volume fraction of each constituent spatially. TF-SOFCs were fabricated with such electrolyte membranes by employing porous metallic electrodes (Pt, Ru) on both sides of the structure. Testing was then carried out as a function of temperature up to ~500 °C using fuel (H2 or CH4) and air. Results and Discussion Self-supported square membrane structures having a side length of 160 μm with film thickness of ~100 nm are shown in Figure 1. As seen in the representative images, under the edge clamped boundary conditions for over 25 samples, homogeneous membranes of GDC do not survive while YDZ membranes are mechanically stable. Homogeneous oxide alloy compositions with varying volume fractions of each constituent parent phase are shown between the GDC and YDZ endpoints. After thermal cycling from 25 – 500 °C, only compositions having greater than 50% YDZ survive. This is attributed to the stability of Zr4+ in the matrix, which renders anion non-stoichiometry induced stresses inconsequential from a mechanical standpoint. We will discuss the electrical effects during our presentation. The key aspect of this portion of our study indicates that alloying a stable cation with a multi-valent counterpart can macroscopically reduce the deleterious effects of chemical strain. This observation has been recently confirmed both experimentally and theoretically by Bishop et al.5 Figure 1 A representative set of (YDZ)x(GDC)1-x, where x is the volume fraction of each constituent phase, optical micrographs of self-supported buckled (x > 0) and broken (x = 0) oxide alloy based membranes. An alternative experimental methodology we explore is to compositionally grade YDZ and GDC on the nanoscale. In this framework, the goal is to synergistically combine the desirable attributes of each parent material. That is, mechanical stability from YDZ and electrochemical activity and increased ionic conductivity from GDC. Utilizing this fabrication approach enabled the successful integration of two test YDZ-GDC graded membrane structures that survive thermal and chemically induced stress imparted during processing and high temperature testing. TF-SOFCs were constructed and exhibited high power densities in both H2 and environmentally abundant CH4fuels. We will discuss our transport results using a general effective medium model. Summary We highlight the challenges with nanoscale membranes, originating from chemical-mechanical coupling oxides having complex point defect distributions. YSZ and CGO are utilized to exhibit methods to overcome chemical strain effects. References 1 I. Lubomirsky, Monatsh Chem.140, 1025 (2009) 2 K. Kerman, S. Ramanathan, J. Mater. Res. (2013) DOI: 10.1557/jmr.2013.301 3 A. Atkinson, T.M.G.M. Ramos, Solid State Ionics129, 259 (2000) 4 Y. Wang, K. Duncan, E.D. Wachsman, F. Ebrahimi, Solid State Ionics178, 53 (2007) 5 S.R. Bishop, D. Marrocchelli, W. Fang, K. Amezawa, K. Yashiro, G.W. Watson, Energy Environ. Sci. 6, 1142 (2013)

Electric field tuning of phase separation in manganite thin films

In this paper, we investigate the electric field effect on epitaxial Pr0.65(Ca0.75Sr0.25)0.35MnO3 thin films in electric double-layer transistors. Different from the conventional transistors with semiconducting channels, the sub(micrometer)-scale phase separation in the manganite channels is expected to result in inhomogeneous distribution of mobile carriers and local enhancement of electric field. The field effect is much larger in the low-temperature phase separation region compared to that in the high-temperature polaron transport region. Further enhancement of electroresistance is achieved by applying a magnetic field, and a 250% modulation of resistance is observed at 80 K, equivalent to an increase of the ferromagnetic metallic phase fraction by 0.51%, as estimated by the general effective medium model. Our results illustrate the complementary nature of electric and magnetic field effects in phase-separated manganites, providing insights on such novel electronic devices based on complex oxides.

Electrical conductivity modeling of carbon black/polycarbonate, carbon nanotube/polycarbonate, and exfoliated graphite nanoplatelet/polycarbonate composites

AbstractAdding conductive carbon fillers to electrically insulating thermoplastic polymers increases the resulting composite's electrical conductivity, which would enable them to be used in electrostatic dissipative and semiconductive applications. In this study, varying amounts of carbon black (CB: 2 to 10 wt %), multiwalled carbon nanotubes (CNT: 0.5 to 8 wt %), or exfoliated graphite nanoplatelets (GNP: 2 to 15 wt %) were added to polycarbonate (PC) and the resulting composites were tested for electrical conductivity (EC = 1/electrical resistivity). The percolation threshold was ∼ 1.2 vol % CNT, ∼ 2.4 vol % CB, and ∼ 4.6 vol % GNP. In addition, three EC models (Mamunya, additive, and general effective media) were developed for the CB/PC, CNT/PC, and GNP/PC composites. The general effective media (GEM) model showed the best agreement with the experimental results over the entire range of filler concentrations (above and below the percolation threshold) for all three composite systems. In addition, the GEM model can be easily adapted for composites containing combinations of different conductive fillers. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Dynamic percolation of carbon nanotube agglomerates in a polymer matrix: comparison of different model approaches

AbstractA series of samples with different content of multi‐walled carbon nanotubes (0.5‐7.5 wt%) in polycarbonate was investigated by electrical conductivity measurements. During isothermal annealing of the as‐produced samples in the melt state an increase of the conductivity with time was observed. A similar conductivity recovery was found after a short shear deformation of the melt. The time‐dependent transition from insulating to conductive state is explained by dynamic formation of a conductive network of interconnected carbon nanotube agglomerates. The conductive networks were found to be stable after cooling the samples below their glass transition temperature. Comparison of the room temperature conductivity plotted vs. nanotube content for as‐produced and annealed samples shows a tremendous shift of the insulator‐conductor transition from above 5 wt% to about 0.75 wt%, respectively. For the description of the insulator‐conductor transition three different approaches were tested: classical percolation, general effective medium model (GEM), and Fournier equation. All three models fit the data satisfactory. Dynamic percolation was described by the GEM model coupled to a kinetic equation for CNT agglomeration. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Preparation and characterization of negative temperature coefficient (Ni,Mn)3O4–La(Mn,Ni)O3 composite

The composites made of spinel-structured (Ni,Mn)3O4 and perovskite-structured La(Mn,Ni)O3 were investigated for potential application as negative temperature coefficient (NTC) thermistor. The composites were prepared using the standard ceramic route. The electrical resistivity of the composite at 25°C was found to decrease by one to two orders of magnitude depending the amount of the low-resistivity perovskite phase, while the thermal constant determining the temperature sensitivity of the NTC thermistor was still reasonably large in the range of 4,000 to 3,000 K, and the resistivity drift after annealing at 150°C for 1,000 h in air was relatively small (∼1.2%). The general effective media model was adopted to fit the electrical resistivity data of the composites, giving a value of 0.37 for the percolation volume fraction of the perovskite phase. This work demonstrates that it is possible to tune the electrical resistivity and thermal constant of the spinel-structured oxide through making composite with low-resistivity perovskite-structured oxide.

The Shielding Effectiveness of Composite Media - a Parametric Analysis Supporting an Engineering Perspective

This paper is presented as an example of a parametric approach that may be applied to engineering the radio and microwave properties of composite materials in the context of providing electromagnetic shielding capability. In this case, the composites are formed by a conductive filler component embedded within an insulating material. The effective electromagnetic (permittivity) properties of the composite are modeled under the quasistatic approximation using the McLachlan general effective medium model, which enables the impact of the percolation (insulator-conductor) transition to be explored. Composites within the transition region exhibit a power-law nature to their effective material properties. The power-law exponents may take a range of values above a limiting value set by the dimensionality of the filler particle network within the composite and with the assumption of a perfectly random distribution of filler particles. In practice, the values of the power-law exponents depend on the chemical interactions between the constituents, the processing conditions and the nature of the inter-particle charge transport. The paper demonstrates the implications of different values of power-law exponent in the context of the trade-off between shielding effectiveness and composite thickness.

Correlation between electrical and magnetic properties of phase-separated manganites studied with a general effective medium model

We have performed electrical resistivity and DC magnetization measurements as a function of temperature, on polycrystalline samples of phase-separated La 5/8− y Pr y Ca 3/8MnO 3 ( y=0.3). We have used the general effective medium theory to obtain theoretical resistivity vs. temperature curves corresponding to different fixed ferromagnetic (FM) volume fraction values, assuming that the sample is a mixture of typical metallic-like and insulating manganites. By comparing this data with our experimental resistivity curves we have obtained the relative FM volume fraction of our sample as a function of temperature. This result matches with the corresponding magnetization data in excellent agreement, showing that a mixed-phase scenario is the key element to explain both the magnetic and transport properties in the present compound.