Maxwell-Garnett Model Research Articles

The transmissivity of one-dimensional photonic crystals comprising three phases nanocomposite layer for optical switching purposes

In the present work, we have demonstrated the optical properties of a one-dimensional photonic crystal structure in which silicon (Si) and a nanocomposite material represent the constituent layers. The nanocomposite (NC) layer is designed from nanoparticles (NPs) of silver (Ag) and Indium Tin Oxide (ITO) in a host medium of air. The optical properties of the proposed design have been theoretically investigated using the well-known transfer matrix method (TMM), Maxwell-Garnett model and generalized Rayleigh mixing formula as well. The numerical results deduce that the effective permittivity of the nanocomposite material is strongly affected by the type and filling fraction of the NPs. Moreover, the effect of other related parameters such as the thickness of NC layer, filling fractions of NPs, permittivity of the background dielectric medium, the radius of Ag NPs and carrier density of ITO NPs on the optical characteristics of our design is also considered. We believe that the proposed structure may be useful as optical filters, reflectors, and optical switches.

Terahertz Permittivity of Pressed ZnO and CuO Powder in Polyethylene Pellets: Effect of Porosity

Terahertz (THz) spectroscopy is used to measure permittivity (100 GHz-2.5 THz) of ZnO and CuO powders with low fill factor pressed into pellets in a polyethylene binder. We show that porosity (air) of such pressed pellets has a large effect on effective pellet permittivity (~10%) and on the extracted permittivity of the oxide constituent (~150%). We explore a two-step analysis based on sequential application of different effective medium models, first to account for the air, and subsequently to extract the oxide's dielectric properties. We show that the combination of Vegard's law and the Maxwell-Garnett model is the best combination to account, respectively, for the air and the oxide powders. In this regard, the capacity that this approach has to adapt to each phase's physical characteristics by using multiple EMMs is an advantage. The resulting oxide permittivities are significantly larger than previously reported for such pellets as a consequence of the porosity. We find for the real relative permittivities of CuO and ZnO ~12.1 and ~8.9, respectively, in the THz range.

Rietveld refined structure, ferroelectric, magnetic and magnetoelectric response of Gd- substituted Ni-Cu-Zn ferrite and Ca, Zr co-doped BaTiO3 multiferroic composites

The room temperature magnetoeletric coupling was investigated thoroughly in various xNi0.48Cu0.12Zn0.40Gd0.04Fe1.96O4 + (1-x)Ba0.985Ca0.015Zr0.10Ti0.90O3 multiferroic composites. Ferrite and ferroelectric phase of the composites have been prepared by the standard solid state reaction technique. Structural study was conducted by the X-ray diffraction (XRD) and the Rietveld refinement was adopted for further analysis of the structure. The refined XRD patterns confirmed all composites having a biphasic spinel-perovskite structure with Fd3¯m, and P4mm space group, respectively. Microstructural characteristics of all samples have been analyzed using Field Emission Scanning Electron Microscopy images. The magnetoeletricaly coupled composites is illustrated by an obvious modification in lattice, dielectric, ferroelectric and magnetic properties as a function of ferrite content. The dielectric constant of the composites was found to decrease with the addition of ferrite content in line with the theoretical estimations of the Bruggeman, Maxwell-Garnett, Lichtencker and Looyenga models, respectively. The dielectric constant and initial permeability were calculated theoretically using the different models and compared with the experimental values. The discrepancy between the calculated and experimental values of dielectric constant and initial permeability might be attributed to the diffusion of ions and interaction between two phases of the composites. The ac conductivity analysis revealed that the conduction mechanism is attributed to the small polaron hopping and also obeyed the Jonscher’s power law. Complex impedance was evaluated using the Nyquist plot which ensured the dominance of both grain and grain boundary resistance. The hysteresis loops (M-H and P-E) ensured the typical ferromagnetic and ferroelectric nature for all composites at room-temperature. Magnetic studies show an improvement of initial permeability, relative quality factor and magnetization, whereas magnetic loss gradually reduces with the increment of ferrite content. The maximum magnetoelectric response (~173 mVcm−1Oe−1) was found for x = 0.10 composite that could be utilized in the future multifunctional devices.

A Scaled Effective Medium Theory for Calculation of Resonant and Relaxation Frequency in Magnetic Composites

Scaled Effective Medium Theory (ScEMT) is applied to predict magnetic resonant and relaxation frequency in polymer-magnetic particle composites with favorable comparison to measured data. A single scaling function is identified that uses magnetic particulate resonant and relaxation frequencies, or magnetization and anisotropy field, volume fraction and DC susceptibility as predicted by ScEMT. Previous publications demonstrated that ScEMT improved the prediction of DC susceptibility as compared to classical models. Maxwell-Garnett (MGT) and Coherent Model Approximation (CMA) serve as theoretical baselines for comparison. However, both require separate scaling functions in their prediction of resonant and relaxation. Measured data are presented that suggest a single scaling function of ScEMT is sufficient to calculate both parameters. The paper emphasizes the application of the models and shows a wide range of particulate chemistries. ScEMT calculates susceptibility, resonant and relaxation frequency that agree with measurement. The paper concludes by predicting dispersive permeability that represents improvement over both CMA and MGT models. Future studies will address formulation of an EMT model (s) that describe mixtures of hard and soft magnetic materials mixed in a polymer composite. EMT for composite dielectric properties will be expanded to address the chaining. Early results of that effort will be reported in a separate paper.

Numerical simulation of magnetohydrodynamics nanofluid flow in a semi-porous channel with a new approach in the least square method

Present study deals with the flow of a fluid with added nanoparticles in a semi-permeable channel with a transverse magnetic effect. We have used Maxwell-Garnett and Brinkman models for effective electrical conductivity and viscosity, respectively. Water-based nanofluids with silver and copper nanoparticles have been used in the present investigation. Firstly, governing differential equations have been nondimensionalized with appropriate similarity transformations. We have also proposed an efficient technique to handle coupled differential equations by the weighted residual method (WRM). Here the least square method has been modified to solve coupled linear/nonlinear differential equations. Residual errors are examined graphically to see the efficiency of the proposed scheme. By taking particular values of Hartmann number, Reynolds number, and volume fraction viz. 0.5, 0.5, and 0.05, respectively, it is seen that residual error almost equal to zero in 6th term approximation. Moreover, for validation, present results have been incorporated with previously published works in special cases. Finally, the nature of the solutions has been reviewed by varying the values of the involved parameters. In this regard, the values of volume fraction are taken in between 0.01 and 0.09. Further, the values of the Hartmann number are considered between 0 and 4, and finally, values of the Reynolds number are taken in between 1 and 5.

Study of the effective surface plasmon in a nano-composite of silver nanoparticles with a host ZrO2 in one-dimensional ternary periodic structure for solar cell application

Effective surface plasmons for dielectric properties of nanocomposite (NC) with spherical silver nanoparticles (Ag-NPs) in a host ZrO2 has investigated at different radii and filling fractions of nanoparticles (NPs) using the Maxwell-Garnett model. The optical properties of one-dimensional ternary periodic structure (1-DTPS) containing SiO2, TiO2, and NC with different parameters has investigated using the transfer matrix method (TMM). Moreover, the absorption properties of the considered structure for transverse electric (TE) and transverse magnetic (TM) have been studied at different incident angles and thicknesses of the NC layer. The dielectric and optical properties of the considered structure has affected by surface waves of dielectric layers as well as surface plasmons of Ag-NPs. The optical properties of the 1-DTPS for TE and TM modes has been studied with varying thicknesses of NC and angles of incidence wave. With the optimum values of the optical parameters of NC and Ag-NPs, the proposed ternary periodic structure may be used as a broadband absorber for solar cells.

A Two-Component Heterogenous System with the Formation of the Perflance Threshold due to Inversion of the Matrix Structure

The possibility of determining the magnetic susceptibility of metal inclusions from measured material parameters of binary composites using known mixing models is considered. A model is proposed that considers the inversion of the matrix structure of the Maxwell–Garnett model for a filler concentration close to the percolation threshold. It is determined that restructuring the composite occurs gradually in the region of transition concentrations the width of which is an additional parameter determined from the experiment. The proposed model is compared with the effective medium model in terms of the dependences of complex susceptibility on filling and frequency. The reliability of the model is illustrated by processing the material parameters of composites with carbonyl nickel as a filler measured in the frequency range 0.1–20 GHz.

Comparative study on ethylene glycol based Ag-Al 2 O 3 and Al 2 O 3 nanofluids flow driven by electroosmotic and peristaltic pumping: a nano-coolant for radiators

This paper aims to provide a comparative analysis of hybrid (Ag- Al 2 O 3) nanofluid and Al 2 O 3 mono nanofluid in a convective heat transfer process driven by electroosmotic and peristaltic pumping. Ethylene glycol (EG) due to its strong anti-freezing properties is taken as a base fluid. The features of mixed convection, magnetohydrodynamics, and Joule heating are also comprised in this study. The slip boundary conditions for axial velocity and temperature are employed at the walls of the microchannel in a porous environment and conditions of zero normal mass flux are imposed for the passive control of nanoparticles. This model is composed by using the Buongiorno flow model along with the modified Maxwell-Garnett model for thermal conductivity of hybrid nanofluids and Poisson-Boltzmann distribution for electric potential generated within the fluid medium. The problem is simplified under the approximations of lubrication theory and Debye–Hückel linearization and the numerical computations have been made through Maple 17 code. The graphical results of flow variables for various involved quantities are prepared and presented with a requisite interpretation. Moreover, contour graphs are also plotted for stream function in order to discuss the trapping phenomenon. The addition of a volume fraction of 9% of aluminum dioxide in ethylene glycol tends to raise the thermal conductivity of working fluid up to 28.97% however further addition of a small number of silver nanoparticles increases its thermal conductivity up to 53.57%. Due to this increment in thermal conductance, it is found that the efficiency of Ag- Al 2 O 3 nanofluid in the heat transfer mechanism is better than the Al 2 O 3 nanofluid. It is further reported that EG based hybrid nanofluid (Ag- Al 2 O 3) as nano-coolant is more applicable for radiators and other cooling systems as compared EG based (Al 2 O 3) nanofluid.

Structural composite laminate materials with low dielectric loss: Theoretical model towards dielectric characterization

Organic matrix composite materials exhibit high mechanical properties associated with lightweight. They also provide the ability to embed radiofrequency features, such as microwave antennas, for smart load-bearing structures of various means of transport. Antennas implementation into composite panels requires electrically conductive fabrics for the radiating elements, feeding lines and ground planes embedded into the structural dielectric composite materials with low loss at microwaves. Accordingly, the present study investigates the assessment of the dielectric characteristics, namely the relative permittivity εr and the loss tangent tanδ of composite laminate materials made of E-glass, S2-glass and quartz fabrics infused with epoxy, polyester and urethane acrylate thermosetting resins. The related dielectric characteristics, measured in two operating bands, namely 100 MHz to 1 GHz and 18–26 GHz, are compared with the theoretical values computed from the 2D Maxwell-Garnett model that we have adapted to laminate composite materials. Mechanical characteristics of such composite laminate materials are also investigated. Eventually, the quartz/urethane acrylate laminate is highlighted as a low loss composite material, highly suitable for the fabrication of antennas operating at microwaves.

Thermally stable AgCu alloy disc array for near infrared filters

We investigated the thermal and optical characteristics of AgCu alloy disc (250 and 380 nm in diameter) arrays to produce an optical filter with low near infrared (NIR) transmittance, and compared their properties with those of Ag disc array. Unlike the Ag discs, the AgCu discs remained relatively stable with hillocks after annealing at 500 °C. The Ag and AgCu disc samples had similar transmittance characteristics, showing a global minimum at ~767 nm (for the 250 nm-disc samples) and at ~1081 nm (for the 380 nm-disc samples). Based on finite-difference time-domain (FDTD) simulations, the global minimum was related to localised surface plasmon resonance (LSPR). The Maxwell-Garnett model was employed to interpret the red-shift of the transmittance minima. The calculations showed that a mixture of agglomerated and stable Ag discs, resulting in different n and k values, would be responsible for the red-shift and an increase in the minimum transmittance.

Numerical study of the electroosmotic flow of Al2O3–CH3OH Sisko nanofluid through a tapered microchannel in a porous environment

This article deals with the numerical simulation of the electroosmotic flow of methanol-based aluminum oxide (Al2O3–CH3OH) nanofluid in a tapered microchannel. The shear-thickening attributes of methanol are characterized by the Sisko fluid model. The tapered microchannel walls move with peristaltic wave velocity. Buongiorno model in combination with the Corcione model for thermal conductivity and viscosity is employed to predict the heat transfer characteristics of Al2O3–methanol nanofluid. The Maxwell–Garnett model is employed to compute the effective electric conductivity of nanofluids. The effect of the porous medium in the flow field is signified by modified Darcy’s law. The salient attributes of viscous dissipation and Joule heating caused by electroosmosis are also taken into account. The approximations of the lubrication approach and the Debye–Huckel linearization are invoked in mathematical formulation for considerable simplification of the flow problem. The solutions of the acquired set of nonlinear governing equations are computed numerically through Maple 17. The graphical results for various physical quantities are also presented for physical interpretation and discussion. It is revealed that fluid becomes more viscous for enhancement in the consistency parameter. Furthermore, maintaining a larger temperature difference within microchannel produces a reduction in the concentration of nanoparticles. Temperature and velocity profiles are strongly dependent on the electroosmosis mechanism. The simulated results will be very important for designing biomicrofluidics devices dealing with rheologically complex fluids such as lubricating greases, blood, saliva or mucus.

Maxwell–Garnett model for thermoelectric materials

The paper studies the problem of an extended thermoelectric spheroid placed in a thermoelectric matrix. The external electric field is assumed to be uniform. Despite the nonlinear nature of the equations, the solution of the problem can be found as a sum of Legendre functions and polynomials. The solution obtained is used to find the effective values of electrical and thermal conductivities, as well as the thermopower for a composite medium consisting of a set of randomly located spheroids. As an example of the model application, we consider a composite consisting of spheroidal inclusions MgAg0.97Sb0.99 placed in a matrix of Bi2Te3.

Theoretical investigation of enhanced sensing property in 1D TiO2/SiO2 periodic layers containing a defect layer of the nanocomposite with different radii of silver nanoparticles in the host liquid crystal

In this paper, we have theoretically investigated the effective dielectric permittivity of the nanocomposite (NC) layer of liquid crystal (LC) with silver nanoparticles at different radii using the Maxwell-Garnett model. The optical properties of a one-dimensional periodic structure (1DPS) of TiO2/SiO2 dielectric materials containing defect NC layer, (TiO2|SiO2)3|NC|(TiO2|SiO2)3, with different radii of silver nanoparticles studied theoretically using the well-known transfer matrix method (TMM). The effective permittivity of NC for = 0° and 90° orientation angles of LC is calculated with varying sizes of the nanoparticles because the size of the silver nanoparticles affects the surface plasmon resonance (SPR). The transmission of defect mode wavelength peaks for 0° and 90° orientation angle of the LC is studied for different radii of nanoparticles. Besides this, we have also studied the absorption characteristics of the considered NC defect structure for different orientation of the LC with varying radii of the nanoparticles.

Presenting two new empirical models for calculating the effective dynamic viscosity and thermal conductivity of nanofluids

In this paper, two new empirical equations for calculating the effective dynamic viscosity and thermal conductivity of nanofluids are presented based on a high number of experimental data available in the literature. These two equations present the effective dynamic viscosity and thermal conductivity of nanofluids as a function of the volume fraction (0 ≤ ϕ ≤ 12%), size (10nm ≤ dp ≤ 5μm) and type (Ag, Cu, Al2O3, TiO2, CuO, SiO2, ZnO, MgO, Fe, Fe3O4, Al, AlN, CaCO3) of the nanoparticles, temperature and thermo-physical properties of the base fluid. The proposed models are compared with frequent used models in literature (Brinkman and Maxwell-Garnett models) and found that these classical models severely underestimate the effective viscosity and thermal conductivity of nanofluids. Two proposed models are also compared with some other theoretical models, as those of Chon, Patel, Corcione, Prasher, Koo, Maiga, Masoumi, etc. The results showed that, present models for spherical nanoparticle are in excellent agreement with experimental data and provide more accurate character predictions for thermos-physical properties of nanofluid in comparison with existing models. In addition, five new equations are also proposed using the least squares method for calculating the viscosity of five common working fluids (Water, Glycerol, Ethylene glycol (EG), Propylene glycol (PG) and Ethanol) as a function of the temperature. Beside the pure comparison between these models, two well-known benchmark cases of conjugate natural (Differentially Heated Cavity) and mixed convection (Two-sided Lid-driven Cavity) of nanofluid are chosen in order to investigate the effects of the volume fraction, size and type of the nanoparticles on the fluid flow and heat transfer performance of nanofluids. Easy to use for numerical simulation purposes, covering a wide range of the solid particle size and having high accuracy in predicting thermos-physical properties of nanofluids make these equations useful and practical for the design of various thermal engineering systems such as heat exchangers.

Influence of the size, shape and concentration of magnetic particles on the optical properties of nano-dispersive structures

In the present paper, using the discontinuous Ni films and magnetite magnetic fluids as examples we consider theoretically and experimentally the influence of the structural parameters on the optical properties of the ultrafine structures. The optical properties of nanostructures are represented within the theoretical Maxwell-Garnett model. The behavior of the optical spectra of thin Ni films and magnetite magnetic fluids was explained in the framework of the effective medium approximation in two cases: q < 0.5 and 0.5 < q < 1. In this model an effective refractive index (n+ik) of the nanostructures can be calculated as a function of the εm, q, and particle shapes. This approach demonstrated a good accordance between the experimental results and the theoretical calculations.

Measurement of the local water content of an epoxy adhesive by fiber optic sensor based on Fresnel reflection

This article presents an application of a fiber optic sensor based on Fresnel reflection for the measurement of local water content within an epoxy adhesive immersed in water. The water content is directly calculated from the measured refractive index with the help of a Maxwell-Garnett model which consider spherical water inclusions inside an epoxy matrix. No calibration is needed. Three samples were equipped with fiber optic sensors and immersed in water. The measured water content was compared with a finite element simulation. The remarkable agreement between both validates the proposed method. In an industrial setting, this experimental approach could be used to monitor the aging of an immersed polymer material, bonded joint or composite structure.

Synthesis and analysis of SnO2/ZnO nanocomposites: Structural studies and optical investigations with Maxwell–Garnett model

SnO2 including different concentrations of ZnO has synthesized using spray pyrolysis technique for preparing on glass substrate at 350 °C. Effect of ZnO ratio has been researched to study optical and structural properties of SnO2. X-ray diffraction scheme indicates the presence of different peaks that attribute to a mixture of rutile SnO2 and hexagonal ZnO. The crystallite size of SnO2 decreases as ZnO ratio increases. The synthesized nanocomposites are characterized via field emission-scanning electron microscopy. The reflectance and transmittance in the wavelength range, 200–2500 nm have been measured. The direct band gaps vary from 3.04 to 3.78 eV to show contrary concept to Ubach's energy. The refractive index and extinction coefficient display vibrations due to ZnO ratio effect. Dielectric constants of SnO2 are deduced effectively in terms of ZnO ratio using Maxwell-Garnett ‘s effective medium theory, they are compared with experimental spectra. The optical properties can be interpreted correctly with Maxwell-Garnett theory of small underestimation, indicating that adaptation of optical properties can take place by varying the volume fraction. Our results present good agreement with experimental data.

Measurement of refractive index of powder by prism coupler.

Refractive index of optical material of powder is measured not as easily as a bulk material. Here, the prism coupling technique in combination with the immersion method is proposed to measure the refractive index of an optical material of powder. First, the powder material to be measured was dispersed in α-bromonaphthalene (C10H7Br) liquid to form a suspension mixture. The refractive index of the mixture, together with that of pure C10H7Br, was then measured at the wavelengths of 632.8, 1311, and 1553 nm using a commercial prism coupler. From the measured index values of pure C10H7Br and powder-dispersed mixture, the refractive index of the powder material was obtained on the basis of the Maxwell-Garnett model. Microcrystal powder from a LiNbO3 single-crystal, which has the known refractive index values, has been exemplified to demonstrate the method. The results show that the method is feasible with an accuracy of ±0.05.

Experimental study on thermal conductivity of paraffin-based shape-stabilized phase change material with hybrid carbon nano-additives

Thermal energy storage with Phase Change Materials (PCMs) is one of the most potential technologies for energy storage. However the low thermal conductivity of PCMs reduces the heat exchange rate during melting and solidification cycles. This paper studied the effects of two hybrid Carbon Nano-additives (CNs) fillers, that is, Expanded Graphite-Multi-walled Carbon Nano-tube (EG-MWCNT) and Expanded Graphite- Carbon Nano-fiber (EG-CNF), on the thermal conductivity of Paraffin-HDPE SSPCM. From the viewpoints of synergistic thermal enhancement effect and the interfacial thermal resistance, the principle of enhancing thermal conductivity of Paraffin-HDPE/EG-MWCNT and Paraffin-HDPE/EG-CNF composite PCMs was analyzed. A modified Maxwell-Garnett model with a synergy factor η was proposed, which found excellent agreement between model prediction and the experimental data. Compared with the 5 wt% loading of single CN additive EG, the thermal conductivities of hybrid CNs fillers (EG-MWCNT and EG-CNF) Paraffin-HDPE SSPCM had increased by 60% and 21.2% respectively. Within the scope of mass ratios of hybrid CNs fillers in this paper, Paraffin-HDPE/EG-MWCNT composite PCM exhibited superior performance than Paraffin-HDPE/EG-CNF in thermal conductivity with the optimal mass ratio of EG and MWCNT being 4:1.

An experimental test for effective medium approximations (EMAs)

Aims.The effective medium approximations (EMAs), or the Lorentz–Lorenz, Maxwell-Garnett, and Bruggeman models, largely used to obtain optical properties and porosities of pure and ice mixtures, have been experimentally tested in this work. The efficiency of these approximations has been studied by obtaining the porosity value for carbon dioxide ice grown at low temperatures. An explanation of the behaviour of the experimental results for all temperatures is given. The analysis carried out for CO2can be applied to other molecules.Methods.An optical laser interference technique was carried out using two laser beams falling on a growing film of ice at different incident angles which allowed us to determine the refractive index and the thickness of the film. The mass deposited is recorded by means of a quartz crystal microbalance. Porosity is determined from its equational definition by using the experimental density previously obtained.Results.From the experimental results of the refractive index and density, porosity values for carbon dioxide ice films grown on a cold surface at different temperatures of deposition have been calculated and compared with the results obtained from the EMA equations, and with recent experimental results.Conclusion.The values of porosity obtained with the EMA models and experimentally, show similar trends. However, theoretical values overestimate the experimental results. We can conclude that using the EMAs to obtain this parameter from an ice mixture must be carefully considered and, if possible, an alternative experimental procedure that allows comparisons to be made should be used.