Bruggeman Model Research Articles

A Study of the Effect of a Protein on the Structure of Water in Solution Using Terahertz Time-Domain Spectroscopy.

Terahertz time-domain spectroscopy (THz-TDS) was used to determine the spectra (range = 1.2-120 cm-1) of aqueous solutions of bovine serum albumin (BSA) at pH range 2.5-10. Under each of the selected pH, BSA molecules exist in a different conformation, compared to other pH values. The spectra were used to calculate the functions of the dielectric permittivity of BSA solutions. Dielectric functions of the aqueous phase of BSA solutions were calculated based on the Bruggeman model, without the contribution of BSA itself. Fitting of the dielectric functions was performed using a model which includes three water spectral bands: two relaxation bands with relaxation times of about 8.28 and 0.3 ps and a vibrational band with a maximum of about 180 cm-1. The parameters of these bands were determined through fitting and physical interpretation at the molecular level can be provided for each of them. A comparison between the values of model parameters of solutions with BSA and without BSA allowed to conclude that the main effect of BSA is the formation of strongly bound hydration shells in the immediate proximity to the protein molecule. At the same time, the structure of more distant layers of the hydration shells is destroyed, with an increased formation of free water molecules. Some differences are observed in the effect of different BSA conformations on the aqueous phase of solution. The proposed approach can be generalized and applied for studying of a wide class of biological macromolecules in aqueous solutions.

On the thermal conductivity of CGI and SGI cast irons

The thermal conductivity of Compacted Graphite Iron (CGI) and spheroidal graphite iron (SGI) was established in the temperature range from room temperature up to 500 °C using the experimental thermal diffusivity, density and specific heat values. The influence of nodularity, graphite amount, silicon content and temperature on the thermal conductivity of fully ferritic high-silicon cast irons was investigated. It was found that the CGI materials showed higher thermal conductivity than the SGI materials. The thermal conductivity tended to increase with increasing temperature until it reached a maximum followed by a subsequent decrease as temperature was increased up to 500 °C. Conventional models were applied to estimate thermal conductivity and the predictive accuracy of each model was evaluated. The thermal conductivity could be estimated by the Helsing model. The Maxwell model, Bruggeman model and Hashin–Shtrikman model were also in fair agreement using the thermal conductivity value of graphite parallel to the basal planes in graphite.

Mixed matrix membranes applications: Development of a resistance-based model

In this study, a model for the prediction of the mass transport through ideal mixed matrix membranes (MMMs) for pervaporation and gas separation processes has been introduced. A Resistance-Based (RB) model was used in conjunction with a three-directional Finite Difference (FD) numerical solution to derive a semi-empirical model for calculating the effective permeability of ideal mixed matrix membranes. Predictions of the effective permeability obtained with the proposed model were compared with the estimated permeability for ideal MMMs using numerous analytical solutions such as Maxwell, Lewis-Nielsen, Bruggeman and Hennepe models. The extended RB model was theoretically able to predict accurately the effective permeability of ideal MMMs over a large range of filler volume fraction. Higher deviations were observed between the predictions of the extended RB model and the estimations of the majority of the other models in the case of MMMs containing higher permeable fillers and larger amount of filler material.

Gas permeation modeling of mixed matrix membranes: Adsorption isotherms and permeability models

In order to calculate the permeability of gases in mixed matrix membranes (MMMs) filled with porous particles, the first step is to calculate the permeability of filler particles. Because particle pore sizes of the considered sodium zeolite Y (NaY) in this study is greater than the molecular sizes of the tested gases (CO2 and N2), it is assumed that diffusion of the gases in the zeolite particles is from Knudsen type. Moreover, the gas sorption data (isotherms) were measured experimentally and then fitted with Langmuir and Freundlich model equations to calculate the related constants. Finally, the experimental CO2 and N2 permeabilities of cellulose acetate (CA)/NaY MMMs were compared with the corresponding data predicted by the well‐known permeability models in this field. It was concluded that the Bruggeman model has better predictions among the other models, especially for the higher particle loadings. POLYM. COMPOS., 39:4560–4568, 2018. © 2017 Society of Plastics Engineers

Modified Bruggeman models for prediction of CO2 permeance in polycarbonate/silica nanocomposite membranes

AbstractThe polycarbonate membranes performances are improved by the incorporation of silica nanoparticles into the polymer matrix. Prepared PC/silica nanocomposite membranes with various silica content are considered and the experimental relative permeance of CO2 gas at 200 kPa (2 bar) feed pressure are used as reference in the predictions using the existing theoretical models such as Maxwell‐Wagner‐Sillar, Bruggeman, Lewis‐Nielsen, Pal, and modified Pal models. TEM and BET analysis were used to characterize the silica nanoparticles; FESEM was used to characterize the morphology of the nanocomposite membranes. The TEM image of the silica nanoparticles reveals that the nanoparticles are mostly spherical. BET results reveal that the surface area and pore diameter of the silica nanoparticles are 618.8 m2/g and 0.28 nm, respectively. The existing models have resulted in poor predictions with errors AARE % of 26.52 to 28.02 %. Observation by FESEM image shows that the dispersed particles are surrounded by interfacial voids and rigidified polymer layer. Modified Bruggeman models that consider the interfacial volume show appreciable prediction with AARE 4.59 % being obtained with the pseudo‐two‐phase Bruggeman model. Moreover, when the model considered pseudo‐three‐phase morphology, the AARE % value reduced to 3.92 %. Thus, the contribution due to the interfacial rigidified layer was minimal.

Analytical heat conduction model of a composite material based on complete spatial randomness of filler in base matrix

In this work, we propose a novel analytical model to obtain the thermal conductivity of a composite material comprising of filler particles randomly distributed in a base matrix. The model assumes complete spatial randomness of the filler particles in the matrix and this can be described by Poisson's distribution. This concept has been applied to arrive at the thermal conductivity of a composite material with Aluminium powder as the filler in the Epoxy matrix. The results obtained by the proposed model have been compared with the experimental results as well as with the other established models such as Maxwell model, Bruggeman model, Lewis - Nielsen model, Russell model and Rule of Mixtures. This comparison reveals that the proposed model predicts the experimental results more accurately than the others. Also the proposed model is able to predict the experimental results of thermal conductivity of Aluminium-Epoxy composite over the entire temperature range from 4.2 K to 300 K. When applied to other published experimental data of similar composites, the model is found to predict the results fairly well with minimal aberrations. Due to the non-empirical nature of the proposed model, perhaps it may be useful for the prediction of other properties of composite materials involving the filler in a base matrix.

Production and investigation of layered zinc sulfide(selenide)/insulator nanocomposites

Layered ZnS/SiO2, ZnS/Al2O3, and ZnSe/SiO2 nanocomposites have been studied. It has been shown that the use of the Maxwell–Garnett and Bruggeman models, as well as the Luyengi formula, in the low dispersion region makes it possible to predict the production of films with a given effective refractive index. Calculated values of the refractive index correlate well with experimental data. The maximal discrepancy between the theoretical and experimental values of the refractive index and the maximal value of the depolarization factor depend on the structure and microstrains.

Characterization of the Pore Structure of Functionalized Calcium Carbonate Tablets by Terahertz Time-Domain Spectroscopy and X-Ray Computed Microtomography

Novel excipients are entering the market to enhance the bioavailability of drug particles by having a high porosity and, thus, providing a rapid liquid uptake and disintegration to accelerate subsequent drug dissolution. One example of such a novel excipient is functionalized calcium carbonate, which enables the manufacture of compacts with a bimodal pore size distribution consisting of larger interparticle and fine intraparticle pores. Five sets of functionalized calcium carbonate tablets with a target porosity of 45%-65% were prepared in 5% steps and characterized using terahertz time-domain spectroscopy and X-ray computed microtomography. Terahertz time-domain spectroscopy was used to derive the porosity using effective medium approximations, that is, the traditional and an anisotropic Bruggeman model. The anisotropic Bruggeman model yields the better correlation with the nominal porosity (R2 = 0.995) and it provided additional information about the shape and orientation of the pores within the powder compact. The spheroidal (ellipsoids of revolution) shaped pores have a preferred orientation perpendicular to the compaction direction causing an anisotropic behavior of the dielectric porous medium. The results from X-ray computed microtomography confirmed the nonspherical shape and the orientation of the pores, and it further revealed that the anisotropic behavior is mainly caused by the interparticle pores. The information from both techniques provides a detailed insight into the pore structure of pharmaceutical tablets. This is of great interest to study the impact of tablet microstructure on the disintegration and dissolution performance.

Modeling of the optical properties of porous silicon photonic crystals in the visible spectral range

Optical devices based on photonic crystals are of great interest because they can be efficiently used in laser physics and biosensing. Photonic crystals allow one to control the propagation of electromagnetic waves and to change the emission characteristics of luminophores embedded into photonic structures. One of the most interesting materials for developing one-dimensional photonic crystals is porous silicon. However, an important problem in application of this material is the control of the refractive index of layers by changing their porosity, as well as the refractive index dispersion. In addition, it is important to have the possibility of modeling the optical properties of structures to choose precisely select the fabrication parameters and produce one-dimensional photonic crystals with prescribed properties. In order to solve these problems, we used a mathematical model based on the transfer matrix method, using the Bruggeman model, and on the dispersion of silicon refractive index. We fabricated microcavities by electrochemical etching of silicon, with parameters determined by the proposed model, and measured their reflection spectra. The calculated results showed good agreement with experimental data. The model proposed allowed us to achieve a microcavity Q-factor of 160 in the visible region.

Efective infrared reflectivity and dielectric function of polycrystalline alumina ceramics

Room‐temperature infrared (IR) reflectivity, terahertz transmission and evaluated effective complex dielectric response of four polycrystalline alumina ceramics (corundum) with highly anisotropic grains in the IR range were determined. The spectra were compared with modelled spectra based on the known IR response of sapphire single crystal and Bruggeman and Lichtenecker models of the effective medium approximation (EMA). The results are extremely sensitive to the surface treatment (polishing), but do not depend on the grain size in the range of ∼0.3–1 μm and on the weak doping, needed for processing of optically transparent ceramics. As all the samples show similar grain shapes and topology, no measurable differences among the fully dense samples were observed. Agreement with the modelled spectra is reasonable, but shows a higher effective mode damping. A weak geometrical resonance was revealed near 500 cm−1, better described by the Bruggeman model. The small sample porosity up to 6.2% is revealed mainly as a reduced reflectivity above ∼650 cm−1, which produces weak losses in the high‐frequency range above the TO phonon modes, better described by the Lichtenecker model.

Optical Absorption and Quantum Confinement in Porous Silicon Nanostructures Studied by Chemical Dissolution in HF Solutions and Photoconduction

The progress of the chemical dissolution of porous silicon (PSi) formed from lightly-doped p-type silicon in ethanoic HF solutions was monitored by recording in situ the photocurrent from monochromatic illuminations, which was used as a measure of optical transmission. The relations between dissolution time, porosity, and absorption coefficient were established and the porosity-dependence of the absorption coefficient derived from ∼60% porosity to 100% porosity. The absorption results were discussed considering the Bruggeman model of effective medium approximation and other measurements from the literature, together with the effects of quantum confinement (QC) and surface states. The porosity and spectral dependences of the QC in the absorption spectra were clearly observed. QC in the blue spectral range (<500 nm) was found to require extremely high porosities (>85%), contrary to the red to green region, where QC was identified for the whole porosity range studied. Our procedure allows the continuous exploration of a wide range of porosities, without limitation on the high side, while preserving an ideal hydrogen-terminated PSi surface and very good structural integrity, as PSi is always kept in HF solution and never dried. The study also allows the determination of the dissolution rate of silicon in various HF-based solutions.

Ultraviolet to far-infrared transmission properties of thin film multi-walled carbon nanotube random networks

Thin films of multi-walled carbon nanotubes forming random networks were produced by vacuum filtration method, and their broadband electromagnetic radiation transmittance spectra are presented. Thickness of the nanotube films was between 100 nm and 1 μm, and the transmission properties are demonstrated for the wavelength range from 300 nm to 400 μm. It is observed that transmittance is an increasing function of a radiation wavelength, and for the thickest films it almost saturates above 1 μm wavelength. To explain the experimental results in the ultraviolet–near infrared range, we employed effective medium theory (in the form of symmetric Bruggeman model) correlating properties of multi-walled carbon nanotubes with the effective dielectric function of a nanotube network. The optical properties of a single multi-walled carbon nanotube that were used for calculations were based on ordinary and extraordinary dielectric functions of bulk graphite. The proposed theoretical model has been successfully fitted to the experimental results. It has been also found that despite the fact that radiation undergoes multiple internal reflections at the film interfaces, the transmittance–thickness relation can be still described by exponential decay.

Influence of embedded MoSi2 particles on the high temperature thermal conductivity of SPS produced yttria-stabilised zirconia model thermal barrier coatings

To prolong the lifetime of thermal barrier coatings (TBCs) recently a new method of microcrack healing has been developed, which relies on damage initiated thermal decomposition of embedded molybdenum disilicide (MoSi2) particles within the TBC matrix. While these MoSi2 particles have a beneficial effect on the structural stability of the TBC, the high thermal conductivity of MoSi2 may have an unfavourable but as yet unquantified impact on the thermal conductivity of the TBCs.In this work the thermal conductivity of spark plasma sintering (SPS) produced yttria-stabilised zirconia (YSZ) model thermal barrier coatings containing 10 or 20vol.% of MoSi2 healing particles was investigated using the laser flash method. Measurements were performed on free-standing composite material over a temperature range from room temperature up to 1000°C. Microstructural analysis was carried out by SEM combined with image analysis to determine the size, distribution and area fraction of healing particles. The measurements were compared with the results from microstructure-based multi-physics finite element (FE) models and analytical models (the asymmetric Bruggeman model and the Nielsen model) in order to study the effects of the addition of MoSi2 particles as well as the presence of micro-pores on the apparent thermal conductivity. The results show a strongly non-linear increase in the thermal conductivity of the composite material with the MoSi2 volume fraction and a dependence on the aspect ratio of MoSi2 particles. Interparticle connectivity is shown to play a big role too.

Dust Library of Plasmonically Enhanced Infrared Spectra of Individual Respirable Particles.

This work characterizes collections of infrared spectra of individual dust particles of ∼4 µm size that were obtained from three very different environments: our lab air, a home air filter, and the 11 September 2001 World Trade Center event. Particle collection was done either directly from the air or by placing dust powder from various samples directly on the plasmonic mesh with 5 µm square holes as air is pumped through the mesh. This arrangement enables the recording of "scatter-free" infrared absorption spectra of individual particles of size comparable to the probing wavelengths whose vibrational signatures are otherwise dominated by scattering and dispersive line shape distortions. The spectra are sensitive to the amounts of various infrared active components and analysis using a Mie-Bruggeman model for mixed composition particles provides volume fractions of the components. Inhalation of dust particles of ∼4 µm size has significant health consequences as these are among the largest inhaled into people's lungs. The chemical composition of ∼4 µm respirable particles is of great interest from health, atmospheric, and environmental perspectives as different environments may pose different hazards and spectroscopic challenges.

Modeling the attenuated total reflectance infrared (ATR-FTIR) spectrum of apatite

Attenuated total reflectance (ATR) infrared spectra were measured on a synthetic and a natural fluorapatite sample. A modeling approach based on the computation of the Fresnel reflection coefficient between the ATR crystal and the powder sample was used to analyze the line shape of the spectra. The dielectric properties of the samples were related to those of pure fluorapatite using an effective medium approach, based on Maxwell–Garnett and Bruggeman models. The Bruggeman effective medium model leads to a very good agreement with the experimental data recorded on the synthetic fluorapatite sample. The poorer agreement observed on the natural sample suggests a more significant heterogeneity of the sample at a characteristic length scale larger than the mid-infrared characteristic wavelength, i.e., about 10 micrometers. The results demonstrate the prominent role of macroscopic electrostatic effects over fine details of the microscopic structure in determining the line shape of strong ATR bands.

Experimental investigations and theoretical determination of thermal conductivity and viscosity of TiO2–ethylene glycol nanofluid

Experimental and theoretical investigations of effective thermal conductivity and effective dynamic viscosity of TiO2-ethylene glycol nanofluid are presented in this paper. The nanofluid was prepared by a two step method; synthesizing TiO2 nanoparticles using ultrasound assisted chemical precipitation method and dispersing them in pure ethylene glycol using an ultrasonicator. TiO2-ethylene glycol nanofluid with a nominal diameter of 5-nm at different volume concentrations (0-7%) at room temperature was used in the current study. The thermal conductivity and viscosities of nanofluids are measured and it is found that both thermophysical parameters (thermal conductivity and viscosity) show increasing trends with addition of nanoparticles to base fluids and the thermal conductivity increase is substantially higher than the viscosity at higher volume fraction. The Bruggeman and Einstein models show reasonably good agreement with our experimental results of thermal conductivity and viscosity respectively.

Effects of hollow Zn2SiO4 particles addition on dielectric properties of isotactic polypropylene-HW composites

Hollow willemite (Zn2SiO4) filler particles (HW) were synthesized via a spray pyrolysis method and used to make composites with isotactic polypropylene (iPP). The dielectric constant (ɛr) of iPP/HW composites exhibited slight variations with the addition of the filler having the high crystallinity, while the dielectric loss (tan δ) value decreased significantly, from 20.1×10−4 to 1.78×10−4. As the weight fraction of the HW filler was increased, though the tan δ values of the composites slightly increased but these values maintained on the order of 10−4 because of the highly crystalline filler. The measured ɛr values of the composites were lower than those predicted by the Bruggeman model when using ɛf=6.6 (Zn2SiO4) and ɛm=2.4 (iPP). However, the data could be made to fit the Bruggeman model when ɛf was assumed to be 4.8, suggesting that the air included in the HW filler suppressed the ɛr of the composite. It was also established that the coefficients of thermal expansion and temperature coefficients of dielectric constant of the iPP/HW composites were significantly improved with increasing HW filler concentrations.

Bruggeman's Exponents for Effective Thermal Conductivity of Lithium-Ion Battery Electrodes

Simulations of lithium-ion battery cells are usually performed with volume averaging methods that employ effective transport properties. Bruggeman's model, which is widely used to determine these effective properties, is primarily based on the volume fraction of porous electrodes. It does not consider actual particle shape, size or the topology of constituent phases; these play a crucial role in determining effective transport. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. Three-dimensional finite volume meshes of fully-resolved lithium-ion battery cathode microstructures are reconstructed from scanned images. Effective volume averaged thermal conductivity is then determined from numerical analysis of thermal transport on these meshes. It is shown that the Bruggeman model for effective thermal conductivity must be recalibrated to fit the effective thermal conductivity computed from these detailed simulations. The relevance of these results to effective transport properties typically employed in electrochemical simulations is presented. Commonly used theories for effective thermal transport in composites are evaluated for comparison. Furthermore, it is shown that Bruggeman's exponents yield an important quantitative measure, the connectivity, to characterize the physical path for transport through the underlying phases.

Microwave dielectric properties of composites consisting of MgAl2O4 filler synthesized by molten-salt method and isotactic polypropylene polymer matrix

MgAl2O4 particles were synthesized through the solid-state reaction method (MAO-S) or molten-salt method (MAO-M). The crystallinity, particle size, and crystal structure of spinel-structured MAO-S and MAO-M particles were characterized and these particles used as dielectric fillers were filled into an isotactic polypropylene matrix, up to 30 vol % filler concentration. Significant differences in the degree of inversion (λ), which represents the cation distribution in tetrahedral and octahedral sites, were obtained for MAO-S and MAO-M by solid-state NMR measurements and the λ value of MAO-S fired for 10 h was 0.39, while that of MAO-M fired for 10 h was 0.64. The dielectric constant of MAO-S- or MAO-M-filled composites increased from 2.4 to 3.7 with increasing filler concentration and was consistent with the Bruggeman model. The dielectric loss and thermal conductivity of the composites were remarkably improved by the addition of the MAO-M filler, depending on the increase in the duration of firing, and were 1.74 × 10−4 and 0.62 W/(m·K), respectively. The coefficient of thermal expansion and the temperature coefficient of the dielectric constant of composites also depended on the filler concentration.

Thermal conductivity modeling of U-Mo/Al dispersion fuel

A dataset for the thermal conductivity of U-Mo/Al dispersion fuel made available by KAERI was reanalyzed. Using this dataset, an analytical model was obtained by expanding the Bruggeman model. The newly developed model incorporates thermal resistances at the interface between the U-Mo particles and the Al matrix and the defects within the Al matrix (grain boundaries, cracks, and dislocations). The interfacial resistances are expressed as functions of U-Mo particle size and Al grain size obtained empirically by fitting to measured data from KAERI. The model was then validated against an independently measured dataset from ANL.