Bruggeman Model Research Articles

Influence of Heat Treatment on the Optical Properties of Thermal Evaporated SnO2 Thin Films

In this investigation, the optical properties of the thermally evaporated SnO2 films and their dependence on the heat treatment were studied. The transmittance, T (λ), spectra were measured over the spectral range of 0.2 to 0.8 μm for SnO2 films that were annealed at different temperatures (300, 350, 400, 450, 500, 550 and 600 K) in vacuum for 1h. All films showed high transparency in the visible range and increased with increasing the wavelength. These films have become more transparent after annealing at different temperatures. The optical constants of annealed SnO2 films were obtained by modeling the measured transmission spectra. The best fit modeling of transmission spectra was obtained by applying Drude and OJL models combined with the effective medium approximation Bruggeman model. Increasing the annealing temperatures decreased both the refractive index and the extinction coefficient of the films. While the optical band gap energy increased from 3.05 to 4.11 eV by increasing the annealing temperature from 300 to 600 K, respectively. Analyzing the refractive index dispersion by using the Wemple-DiDomenico model revealed that the oscillator resonance energy Eo decreased whereas the oscillator dispersion energy Ed increased with increasing the annealing temperature.

Far-infrared spectroscopic study of CeO2 nanocrystals

We present the far-infrared reflectivity spectra of 5 nm-sized pure and copper-doped Ce1−xCuxO2−y (x = 0; 0.01 and 0.10) nanocrystals measured at room temperature in the 50–650 cm−1 spectral range. Reflectivity spectra were analyzed using the factorized form of the dielectric function, which includes the phonon and the free carriers contribution. Four oscillators with TO energies of approximately 135, 280, 370, and 490 cm−1 were included in the fitting procedure. These oscillators represent local maxima of the CeO2 phonon density of states, which is also calculated using the density functional theory. The lowest energy oscillator represents TA(L)/TA(X) phonon states, which become infrared-active Eu modes at the L and X points of the Brillouin zone (BZ). The second oscillator originates from TO(Γ) phonon states. The oscillator at ~400 cm−1 originates from Raman mode phonon states, which at the L point of BZ also becomes infrared-active Eu mode. The last oscillator describes phonons with dominantly LO(Γ) infrared mode character. The appearance of phonon density of states related oscillators, instead of single F2uinfrared-active mode in the far-infrared reflectivity spectra, is a consequence of the nanosized dimension of the CeO2 particles. The best fit spectra are obtained using the generalized Bruggeman model for inhomogeneous media, which takes into account the nanocrystal volume fraction and the pore shape.

Modelling in mixed matrix membranes for gas separation

Various gas permeation models including Maxwell model, Bruggeman model, Lewis‐Nielson model and Pal model were compared via a modelling approach with the relative permeance of CO2 against published experimental data on silica filled polysulfone/polyimide (PSF/PI) mixed matrix membranes (MMMs). However, none of the tested models were able to predict the data with good accurately. A closer look at the cross‐sectional image by scanning electron microscopy (SEM) indicated that the fillers were actually prolate ellipsoids dispersed within the matrix. Maxwell‐Wagner‐Sillar model was then employed to investigate the prolate effect and it was observed that the optimization curves of maximum packing (φm) and shape factor (n) showed least deviations. The percentage average absolute relative error (AARE %) value for fitted shape factor (nf) was found to be in the range of 1.12–2.17 at 2–10 bar pressure which showed its robustness. A further evaluation from SEM image showed that the shape factor along z‐direction (nz) displayed a minimum deviation of 17.52 % for prolates at 0.102 ± 0.01. By using nz as upper limit and estimated shape factor ne through generalization, the error was reduced to 6.01 %. The AAR % deviation was found in the order of nf <ne < nz,which indicated the importance of shape factor parameter for estimating true CO2 permeance.

High frequency magneto-dielectric effects in self-assembled ferrite-ferroelectric core-shell nanoparticles

Magneto-dielectric effects in self-assembled core-shell nanoparticles of nickel ferrite (NFO) and barium titanate (BTO) have been investigated in the millimeter wave frequencies. The core-shell nano-composites were synthesized by coating 100 nm nickel ferrite and 50 nm barium titanate nanoparticles with complementary coupling groups and allowing them to self-assemble in the presence of a catalyst forming heterogeneous nanocomposites. Magneto-electric (ME) characterization of as-assembled particles has been carried out by measurements of the relative permittivity ɛr as a function of frequency f under an applied static magnetic field H over 16–24 GHz. Measurements show an H-induced decrease in ɛr of 1 to 1.5%. But a giant magneto-dielectric effect with an H-induced change in permittivity as high as 28% is measured under dielectric resonance in the samples. A strong ME coupling was also evident from H-tuning of dielectric resonance in the composites. A theory for the high frequency magneto-dielectric effect has been developed and consists of the following steps. First the Bruggeman model is used to estimate the effective dielectric constant for the shell consisting of the BTO particles and voids considered as spherical air-pores. Then the permittivity for the core and shell is estimated taking into consideration the sample porosity. Finally the H-dependence of the permittivity due to ME interactions is calculated from the free energy considerations. Estimated ɛr vs. H and dielectric resonance frequency vs. H characteristics are in general agreement with the data.

Effect of packing density on flame propagation of nickel-coated aluminum particles

The combustion-wave propagation of nickel-coated aluminum particles is studied theoretically for packing densities in the range of 10–100% of the theoretical maximum density. Emphasis is placed on the effect of packing density on the burning properties. The energy conservation equation is solved numerically and the burning rate is determined by tracking the position of the flame front. Atomic diffusion coefficients and reaction rate of isolated nickel-coated aluminum particles are input parameters to the model. The burning behaviors and combustion wave structures are dictated by the heat transfer from the flame zone to the unburned region. Five different models for the effective thermal conductivity of the mixture are employed. The impact of radiation heat transfer is also assessed. As a specific example, the case with a particle size of 79μm is considered in detail. The burning rate remains nearly constant (<1cm/s) up to a packing density of 60%, and then increases sharply toward the maximum value of 11.55cm/s at a density of 100%. The Maxwell–Eucken–Bruggeman model of thermal conductivity offers the most accurate predictions of the burning rate for all loading densities.

Gas Permeation Models in Mixed Matrix Membranes for Gas Separation

Various theoretical models on CO2 permeation were discussed that included Maxwell model, Bruggeman model, Lewis-Nielson model and Pal model. These models were used for comparing the relative permeance of CO2 with the previously published experimental data on silica nanoparticles filled polysulfone/polyimide (PSF/PI) mixed matrix membranes (MMMs). The results showed that the deviation was in the increasing order: Lewis-Nielsen model&lt; Maxwell model&lt; Pal model&lt; Bruggeman model. All these models assumed that the fillers are spherical in shape. A scanning electron microscope (SEM) cross-sectional image indicated that the silica particles were prolate ellipsoids that were dispersed in the matrix. To investigate the prolate effect, the Maxwell-Wagner-Sillar (MWS) model was employed. The evaluation from cross-sectional image of the membrane structure indicated that the shape factor along z-direction gave a minimum deviation of 17.52%-20.10% at 2-10 bar feed pressure respectively.

Enhanced gas separation properties of metal organic frameworks/polyetherimide mixed matrix membranes

ABSTRACTMetal organic frameworks (MOFs) are supposed to be ideal additives for mixed matrix membranes (MMMs). In this article one kind of MOFs, Cu3(BTC)2, is synthesized, then directly incorporated into a model polymer (Ultem®1000) using N,N‐dimethylacetamide as solvent. Cu3(BTC)2 particles are uniformly dispersed and there are no interfacial defects in the prepared MMMs when Cu3(BTC)2 loading is not more than 35 wt %, seen in SEM images. Pure gas permeation tests show that gas permeability increases obviously with Cu3(BTC)2 loading increase, while ideal selectivities of CO2/N2 and CO2/CH4 are almost unchanged. For MMM with the best separation property, CO2 permeability increases about 2.6 times and CO2/N2 selectivity remains almost unchanged. Results about gas diffusivity and solubility indicate that gas diffusivity and solubility make contribution to gas permeability increase at the same time but in different ways. Gas permeation properties of MMMs are well predicted by Maxwell or Bruggeman model. © 2014 The Authors Journal of Applied Polymer Science Published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40719.

Inhomogeneity structure and the applicability of effective medium approximations in calculating light scattering by inhomogeneous particles

Atmospheric aerosols commonly occur as inhomogeneous particles with significant internal variations of refractive indices. For the purpose of light-scattering calculations, effective medium approximations (EMAs) have been developed that seek to model an inhomogeneous particle with an internal variation of refractive index using a homogeneous particle with a single “effective” refractive index, one whose value is expected to yield approximately the same scattering properties. Here the applicability of four EMAs is investigated in the relatively simple case that the particle is a mixture of materials having just two different indices of refraction, and consideration is given to the effects of the spatial arrangement of these on the reliability of results obtained using the EMAs. The EMAs considered are based on the Bruggeman theory, the Maxwell–Garnett theory, and two different Wiener bounds. The mixing states considered are relatively regular forms of “layering,” as well as states that involve varying degrees of more irregular “mixing.” Just two overall particle shapes are considered: spheres and spheroids. For each inhomogeneous particle two sets of scattering calculations are performed: calculations treating the inhomogeneous particle itself exactly, and calculations treating an effective homogeneous particle with the same shape and size but a single refractive index determined using one of the EMAs. The first kind is done using the core–mantle Mie theory in the case of stratified composition and the pseudo-spectral time-domain method in the more irregular mixing cases. The second kind of calculation is done using the Lorenz–Mie or T-matrix method.Calculated values of extinction efficiencies, asymmetry factors, and phase matrices of both a single particle and an ensemble of particles are compared. In comparisons of the EMAs with each other, the Bruggeman model and Maxwell–Garnett model give similar results, results which differ by small but noticeable amounts from the results obtained from the Wiener bounds. This suggests that the particular choice of one of the EMAs over another is not critical in calculating the scattering properties of atmospheric particles, especially the bulk-scattering properties. Comparison with the numerically exact results shows that the applicability of the EMAs is largely independent of the particle shape, size, or volume fraction of the components, but is significantly affected by different mixing states. It is found that the Bruggeman and Maxwell–Garnett theories can only give accurate approximations for the optical properties of well-mixed particles, ones for which the scale characterizing the index variation is no larger than about 0.4/π times the wavelength of the incident light, and that applicability of EMAs for stratified and weakly mixed particles is very limited. These results must of course be viewed with some caution, given the great number of combinations of particle geometries, mixing states, and refractive indices that are possible compared to the few idealized ones we examine.

Molecular Interaction study of Multi-Functional Group of Alcohols through Dielectrics Using TDR

The complex permittivity spectra for tert-butyl alcohol(TB) with n-propanol(nP) were determined over the frequency range of 10 MHz to 20 GHz using the time domain reflectometry (TDR) in the temperature range of 25°C to 55°C for 11 different concentrations of the system. The static dielectric constant (ε0) and relaxation time (τ) have been determined these spectra using the Debye model. Excess properties and Kirkwood correlation factor of the mixtures have been determined. The excess permittivity is found to be positive in the tart-butyl alcohol rich region and negative in the n-Propanol rich region. However, the excess inverse relaxation time has different trend. The static dielectric constants for the mixtures have also been fitted with the modified Bruggeman model by assuming an additional parameter in the model.

Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques

We report on the non-destructive quantification of the porosity of pharmaceutical compacts (microcrystalline cellulose tablets) by using both optical and terahertz techniques. For the full analysis of the porosity of pharmaceutical tablets, the results obtained in both cases have shown that optical and terahertz techniques are complementary. The intrinsic refractive index of microcrystalline cellulose was estimated using the effective refractive index obtained from the time delay of the THz pulse together with the Bruggeman model for effective media. Once this intrinsic refractive index is known, the unknown porosity of the tablet can be estimated with the aid of the measured effective refractive index as well as the thickness of the pharmaceutical tablet. The method was tested using a set of thirteen tablets having different porosities. It is shown that the error in the estimation of the unknown tablet's porosity is less than 1%. In addition, surface roughness was measured by using an optical interferometer and gloss by using a diffractive-optical-element based glossmeter. The measurement was achieved by scanning the tablets with a probe beam and detecting the reflected light. The surface roughness and gloss data show relatively good correlation with the porosities of the tablets.

Enhanced Thermal Conductivity in Polyimide/Silver Particle Composite Films Based on Spontaneous Formation of Thermal Conductive Paths

A series of polyimide (PI)/silver composite films incorporating μm-sized metallic silver particles (Ag-MPs) were prepared using matrices of sulfur(SD), fluorine(TF), and siliconcontaining (SIM) PIs as well as an immiscible blend of SDand TF-PIs (b-SF). The thermal conductivity (λ ) of the composited films accords well with the calculated value (λcal) based on the Bruggeman model below the particle contents ( ) of 30 vol%, whereas the composite films of SD/Ag and b-SF/Ag exhibited extraordinarily larger λ values than λcal in the range of >30 vol%. Moreover, the λ s of SD/Ag films with uniform dispersion of Ag-MPs are almost equivalent to those of b-SF/Ag films in which Ag-MPs are selectively dispersed in the SD phase. In contrast, the λ s of SIM/Ag films with homogeneous dispersion accord well with the λcal and much smaller than those of SD/Ag and b-SF/Ag. These facts indicate that effective thermal conductive paths were spontaneously generated in SD/Ag films as well as in b-SF/Ag films.

A semi-analytical model for the thermal conductivity of nanofluids and determination of the nanolayer thickness

Nanofluid shows a huge potential to be the next-generation heat transfer fluid since the nanoparticles can suspend in the base fluids for a long time and the thermal conductivity of the nanofluid can be far above those of convectional solid–liquid suspension. It has long been known that liquid molecules close to a solid surface can form a layer which is solid-like in structure, but little is known about the connection between this layer and the thermal properties of the suspension. In this study, a semi-analytical model for calculating the enhanced thermal conductivity of nanofluids is derived from the steady heat conduction equation in spherical coordinates. The effects of nanolayer thickness, nanoparticle size, volume fraction, thermal conductivity of nanoparticles and base fluid are discussed. A linear thermal conductivity profile inside the nanolayer is considered in the present model. The proposed model, while investigating the impact of the interfacial nanolayer on the effective thermal conductivity of nanofluids, provides an equation to determine its nanolayer thickness for different types of nanofluids. Hence, different relationships between the nanolayer thickness and the nanoparticle size are found for each type of nanofluid. Moreover, based on the present model’s prediction, it is found that the effective thermal conductivities of nanofluids show the same result as the Maxwell model when the nanolayer thickness value approaches to zero. Lastly, the effective thermal conductivities of different types of nanofluids calculated by the present model is in good agreement with the experimental results and the prediction is much better than the Maxwell model and Bruggeman model.

Effect of sonication time on enhancement of effective thermal conductivity of nano TiO2–water, ethylene glycol, and paraffin oil nanofluids and models comparisons

This paper presents experimental and theoretical determination of the effective thermal conductivity of various base fluids and nano TiO2 composition. Ultrasonically assisted sol–gel method was used for synthesising anatase TiO2 nanoparticles and dispersing them into base fluids using sonication for the synthesis of nanofluids. It is observed that thermal conductivity enhancement is significantly higher than that of base fluid. The thermal conductivity shows an increment with the addition of nanoparticles and confirms a 22% enhancement achievable in base fluids. The effect of base fluids is a complex idea and difficult to understand; lower base fluid viscosities were supposed to contribute higher in enhancement of thermal conductivity, but another important factor; i.e. fluid nanoparticles surface interaction, nanoparticles crystal type also contributes in enhancement. In the further study, as the sonication time increases; an improvement in the thermal conductivity of nanofluids is also observed. Except water-based nanofluids, all others show reasonably good agreement with the data predicted by Bruggeman model and the prediction is in the range of 5%. This study is important since it covers base fluids with a wide range of thermal conductivity and viscosity.

Comparison of Two‐Phase Thermal Conductivity Models with Experiments on Dilute Ceramic Composites

Thermal shock resistance of cubic 8 mol% yttria‐stabilized zirconia (YSZ) can be increased by the addition of dilute second phases. This study addresses how these dilute second phases affect the thermal conductivity for two‐phase ceramic composites of 8 mol% YSZ with 10–20 vol% alumina (Al2O3) or 10–20 vol% mullite (3Al2O3·2SiO2). Thermal conductivity measurements from 310 K (37°C) to 475 K (202°C) were made using the 3ω method and compared with results from 3D analytical models and a 2D computational microstructure‐based model (Object‐Oriented Finite Element Analysis, OOF2). The linear Rule of Mixtures was the least accurate and significantly overestimated the measured thermal conductivity at low temperatures, with errors in some cases exceeding 100%. Calculations using the Bruggeman and OOF2 models were both much better, and the deviation of less than ±2.5% across all compositions and temperatures is within the range of experimental and modeling uncertainty. The Maxwell Garnett equation was a close third in accuracy (±8%). A sensitivity analysis for each model quantifies how small perturbations in the thermal conductivity of the dispersed second phase influence the effective thermal conductivity of the composite, and reveals that the linear Rule of Mixtures model is physically unrealistic and oversensitive to the thermal conductivity of the dispersed phase.

Effect of the hydrogen concentration on the growth mechanism of sputtered hydrogenated silicon thin films

The method of elastic recoil detection (ERD) has been utilized to analyze the actual hydrogen concentration in hydrogenated silicon thin films and has been demonstrated to provide more stable and accurate analysis for quantification of the hydrogen concentration than does Fourier Transform Infrared Spectroscopy. In order to realize the quality of thin films, spectroscopic ellipsometry and the applied effective medium approximation (EMA) theory of the Maxwell-Garnett and Bruggeman models are applied to deducing the effective refractive index of the films. The relative void fractions corresponding to amorphous silicon films with lowest hydrogen flow could be obtained based on the EMA theory. Therefore, this study found an important linear relationship between the hydrogen concentration and structural relaxation as a consequence of the void fraction induced by the hydrogen flow.

Theoretical and experimental studies on the gas transport properties of mixed matrix membranes based on polyvinylidene fluoride

The effects of the impregnation of three types of inorganic fillers into polyvinylidene fluoride (PVDF) polymer membranes on the gas permeability and selectivity of these membranes were studied theoretically and experimentally. Permeabilities of He, CO2, O2, and N2 through three types of mixed matrix membranes (MMMs) based on PVDF, that is, PVDF/SiO2, PVDF/MCM‐41, and PVDF/4A MMMs, were experimentally measured and theoretically predicted using Maxwell, Higuchi, Bruggeman, and Bottcher‐Landauer models. Theoretical permeabilities of the PVDF/SiO2 MMMs using the above four models predicted the results in the following order: Maxwell model&gt;Bruggeman model&gt;Bottcher model&gt;Higuchi model. However, this sequence was reversed for PVDF/MCM‐41 MMMs. The nonporous SiO2, mesoporous MCM‐41 and zeolite 4A inorganic fillers had effects on the permeabilities of the challenge gases for the PVDF/SiO2, PVDF/MCM‐41, and PVDF/4A MMMs but had no effects on the selectivities of the MMMs. The experimental permeabilities of the MMMs showed that there were no significant differences among the three types of MMMs despite that the inorganic fillers, that is, SiO2, MCM‐41, and zeolite 4A, had distinct dissimilar properties such as pore structures and particle sizes. Density measurements indicated that some voids were present in the polymer/particle interfaces. Based on the density measurement results, the void volume fractions of the resulting MMMs were calculated. An equation is derived to determine the void thickness of the MMM in terms of its physical properties and hence this proposed equation can substitute the difficult task of measuring such void thickness through any microscopy techniques. The Maxwell, Higuchi, Bruggeman, and Bottcher‐Landauer models could not predict the actual gas permeabilities of the PVDF MMMs. By taking the effects of crystallinity and immobilization factor on gas permeability into consideration, the extended modified Maxwell model showed good agreement with the experimental gas permeabilities of the resulting MMMs, indicating that the model did capture the essence of the gas transport behaviors through the MMMs. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4715–4726, 2013

Refractive Index Estimation of Nanoporous Silicon in Visible and Near-Infrared Spectrum Range

In this paper, we use Bruggeman model to calculate refractive index of nanoporous silicon, which was fabricated by electrochemical etching. The calculated result shows that the refractive index of the nanoporous silicon decreases linearly with increasing porosity and etching current density. In addition, the refractive index of nanoporous silicon was also measured by spectroscopic ellipsometry in the visible light spectrum range. The measured refractive index and extinction coefficient were in agreement with the calculated data, after being modified by the refractive index modified model of heavily doped silicon. In particular, we estimate the refractive index at the optical wavelengths in visible and near-infrared spectrum ranges, which may be widely used in various types of optical sensors and optoelectronic devices for optical communication systems.

Optical constants correlated electrons-spin of micro doughnuts of Mn-doped ZnO films

Diluted magnetic semiconductor (DMS) Mn:ZnO thin films with “ring-like or doughnut-like” structures were grown using aerosol spray pyrolysis for 20 and 30min. Electron paramagnetic resonance revealed the ferromagnetic ordering which varies with Mn concentration. These ferromagnetic films obtained coexist with dielectric state. Spectroscopic ellipsometry results showed that the dielectric constants ɛ1 and ɛ2 also vary in definite pattern as Mn concentration. We used and fitted Bruggeman theory to explain these trends and to find ɛ1 and ɛ2 for both ZnO and Mn which compare well with literature. The results showed that the structural, optical and magnetic properties of these DMSs are strongly sensitive to the preparation parameters. It is unambiguously demonstrated that the room-temperature ferromagnetism is strongly correlated with dielectric constants. The effective medium approach Bruggeman model used to fit our experimental data demonstrated a decrease in the dielectric constant with the addition of Mn concentration. These findings revealed that the refractive index of the films increases with ferromagnetic ordering while the extinction coefficient reduces. This indicates that when the Mn:ZnO film becomes more opaque (high reflecting) to UV (∼370nm) and absorbs less of that light, the ferromagnetic ordering is enhanced. A relatively new phenomenon of d-band resonance at 3.35eV (∼370nm polarized light) from ZnO:OMn molecule at 0.25at.% Mn was observed for both 20 (thinner film) and 30min (thicker film) deposited Mn:ZnO films. A good correlation between ferromagnetic intensity signal with its width and angular dependence for the films was also observed.

Optical Properties of Au Nanoparticles Included in Mesoporous TiO2 Thin Films: A Dual Experimental and Modeling Study

Gold nanoparticles (NP) were synthesized inside ordered mesoporous TiO2 thin films (MTTF) by stepwise reduction of AuCl4– with NaBH4. This leads to an optical material (Au@TiO2) of interest for plasmonic applications. The films (pure titania or gold-titania nanocomposites) were thoroughly characterized by UV–visible and ellipsometry spectroscopies. The dielectric function of the MTTF, considered as the dielectric environment in which the NP are embedded, was acquired by ellipsometry and rationalized by the asymmetric Bruggeman model as an effective medium formed by the mixture of dense TiO2 and air. Nanocomposite Au@TiO2 systems present an isotropic dispersion of Au NP in the 5–8 nm range. The UV–visible spectra obtained with a low nanoparticle filling fraction of the pore volume (fNP < 2%) are accurately reproduced by both Maxwell–Garnett (MG) and Mie theories. Accurate and coincident values of fNP and NP size are obtained by this method. The dielectric function of Au NP used in this work was studied in ...

Baric polymorphism: characteristic functions and critical indexes

Polymorphous phase transition induced by hydrostatic pressure has been considered as a percolating process. Host matrix of the initial solid phase with nuclei of a new phase arising therein due to phase transformation was treated as an inhomogeneous medium. Electrical conductivity of the medium was the control parameter for searching over the stage of phase transformation. Effective-medium approximation, based on the Bruggeman model, has been improved to fit with percolation theory postulates. Functional connections between volume fraction of a new polymorphous phase and a pressure value were calculated for three investigated cases: n-ZnO, n-GaAs, and n-InAs on the base of the proposed approach.