Maxwell-Garnett Equation Research Articles

Analytical study of gold-DNA nano core-shell cloaking characteristics for drug delivery and cancer therapy.

The cloaking characteristics of biocells can be considered as a factor to determine drug absorption by the tissues. The metal-organic core-shell structure can act as a cloak around the molecules of tissue and can be used as a nanomachine for drug delivery. Thus, we define a ratio of drug absorption based on frequency red-shift and the effective permittivity in the optical spectrum. Here, a cylinder of molecules coated by plasmonic nano core-shells is proposed for measuring the cloaking characteristics of biocells. The overall bandwidth of the proposed cloak for reflectance less than -10 dB is 36%. We check the effect of the filling factors of nanoparticles on the reflection and the frequency response of the tissue. Besides the frequency red-shift and change in the level of reflection, the phase and impedance are extracted. We could obtain the normalized scattering cross-section of 5 dB lower than the cylinder without cloak for the cylinder with a gold-DNA core-shell cloak. Here, we modify the Maxwell-Garnett equation for a cylindrical structure to obtain the effective value of the permittivity for cancer and normal tissues. The results show that obtained permittivity from the simulation has a good match with the calculated permittivity from the Maxwell-Garnet equation. Therefore, this approach can be considered as an efficient method for drug absorption and diagnosis of cancer cells from normal cells.

1-D Magnetic photonic crystal as intermediate reflective layer in tandem solar cells

The analysis of the optical properties of a 1-D binary magnetic photonic crystal (MPC) made up of Cu-doped YIG, a metal-doped magnetic composite material as one layer, and μc-SiOx:H as another layer is carried out. The refractive index of the Cu-YIG nanocomposite system is calculated using the Maxwell-Garnett equation. The transmission spectra of 1-D MPC is studied using the Transfer Matrix Method. The proposed 1-D MPC is designed in such a way that it is suitable to act as an intermediate reflective layer (IRL) in thin-film silicon tandem solar cells. The reference Bragg wavelength (λB) is set at 500 ​nm. The effect of copper doping in the magnetic photonic crystal on the photonic bandgap is studied. By varying the number of periods and the percentage of copper doping, the changes in the photonic bandgap are analysed. It is found that the photonic bandgap increases with the number of periods of the MPC and the percentage of copper doping, which tends to enhance the light trapping in tandem solar cells.

Hydrogen diffusivity in different microstructural components in martensite matrix with retained austenite

We elucidate the hydrogen diffusivity in martensite matrix with retained austenite (RA). Two aspects are focused: effect of microstructure on hydrogen diffusion behavior; hydrogen diffusivity calculation for different microstructural components. Quenched martensite (QM) had the highest effective hydrogen diffusion coefficient because of high dislocation density. Effective hydrogen diffusion coefficient decreased with the increase of intercritical annealing temperature because of decrease in dislocation density and increase of RA. According to the principle of Maxwell-Garnett equation, the hydrogen diffusion coefficient for grain boundary (GB) was 7.99 × 10−8 m2/s and hydrogen diffusion coefficient of tempered martensite (TM) was 7.84 × 10−11 m2/s.

Optical model to describe coherent transmittance of polymer dispersed liquid crystal film doped with carbon nanotubes

An optical model has been developed for analyzing the coherent transmittance of a polymer dispersed liquid crystal films doped with carbon nanotubes (CNTs) at uniform normal droplet-polymer interface anchoring. It is based on the Foldy–Twersky and anomalous diffraction approximations, Maxwell-Garnett equations, and the order parameters concept. The model allows one to analyze the electro-optical response of films depending on their thickness, the refractive indices of the liquid crystal (LC) and polymer matrix, size and concentration of the LC droplets, concentration of nanotubes, conductivities of the LC and the polymer. Experimental verification of the model is performed.

Investigation of latent heat storage system using graphite micro-particle enhancement

Low-temperature energy storage system (LTESS) stores the thermal energy from the sun, exhaust gases and waste heat from industries and other sources. Phase changing materials (PCM) are used as the energy storage medium for this system. The advantage of PCM is that it has higher energy storage density, with low volume. The disadvantage of PCM for using as LTESS is that the thermal conductivity of PCM is less and this requires more time period and surface area of contact, for loading and unloading of thermal energy. A solution to this problem can be incorporating graphite micro-particles in the paraffin PCM to improve its thermal conductivity. The heat transfer of LTESS is determined experimentally. Incorporating micro-particle in the PCM has improved the heat transfer of the LTESS. Maxwell–Garnett equation is used to determine the heat transfer of PCM and J-type temperature measuring probe, and sensor apparatus is used to determine the heat transfer experimentally. The encapsulation has increased the heat-retaining ability and storage time by about 40% on average for the flow rates tested.

Ellipsometric study of optical properties and oxidation processes of compacted powders based on aluminum alloys

The paper presents the results of an ellipsometric study of compacted powders of aluminum-based binary alloys containing 1,5 wt.% of rare earth elements (Sc, La, Ce, Sm) and cast aluminum-silicon alloys with the following compositions: Al–10Si–0,5Mg– 0,3Fe–0,1Ca and Al–12Si–0,6Mg–0,5Fe–0,5Ca–0,45Na. An immersion method was used to determine the optical constants of massive polycrystalline alloys obtained by remelting these powders in vacuum, as well as their oxide films for a wavelength λ = 0,6328 μm. Using the optical constants of these alloys, the dependence of their reflectivity on the surface oxide film thickness was calculated. It was found that an increase in the amount of the alloying component and intermetallic phases in the alloy decreases its reflectivity. In addition, the optical constants were used in the construction of modified Δ–ψ nomograms calculated using the Maxwell-Garnett equation that make it possible to determine the thicknesses of oxide films on particles and the volume fractions of metal in compacted powders, and to study the processes of their oxidation in air. It was shown that oxidation of aluminum ASD-4 powders and Al–1,5% REM binary alloys at 600 °C is described by a simple model where a decrease in the metal fraction leads to an increase in the oxide film thickness. It turned out that the oxidation of aluminum-silicon alloys is much faster and not described by this model, which may be due to the appearance of a liquid phase in the powder. A large number of metal droplets on the surface of particles increase the amount of metal on the studied tablet surface in general. The high oxidation rate of aluminumsilicon alloys in air can be explained by the surface activity of magnesium in relation to liquid aluminum.

Aspect and mass ratio dependence of microwave heating in silicon carbide fibers at 2.45 GHz

Silicon carbide is a key material in microwave (MW) processing and is widely employed as an MW absorber and catalytic agent. In this study, we experimentally improve the MW absorption properties of SiC particles at frequencies of 2.45 GHz by considering the shapes of fibers. We heated SiC fibers using MW radiation and their heating behaviors were then compared with their MW absorption properties. The heating behavior of the fibers was dependent on their aspect ratio; this result was in accordance with theoretical predictions. Furthermore, the mass ratio dependence of the MW heating behavior was investigated by employing an Al2O3-SiC fiber mixture. Their absorption properties exhibited peak MW absorption at specific relative densities under Emax and indicated different behavior from that predicted by the Maxwell–Garnett equation.

Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver

Optical properties of well-known bulk materials can be significantly modified by decreasing dimensions to nm-size. Using Molecular Beam Epitaxy (MBE) and e-beam Physical Vapour Deposition (PVD) we have fabricated 20–30 nm-thick amorphous Ge, Te and Se films. The permittivities of investigated layers have been extracted from measurements of the Ψ and Δ ellipsometric azimuths. We found that for all of the investigated films, the intensity of all bands in the permittivity spectrum is smaller than for bulk materials or thick (> 100 nm) films. Using the acquired optical constants along with the permittivity of a 20 nm-thick silver film, we have applied the Maxwell-Garnett equation to predict the permittivities of a silver film with Ge, Se or Te segregated in its structure. Implementing the parameters of 20 nm-thick Ge results in an 81 nm redshift of the segregation-induced band with respect to the experimental value, while implementing the parameters of 2 nm-thick Ge film results in a 95 nm blueshift of this band.

Prediction of dielectric constant and loss for some polypropylene - additive compounds

In order to influence properties of polymers, several different type of additives can be used. Often, time consuming experimental work is needed to assess performance and suitable concentrations for the chosen polymer-additive system. Therefore, it is preferable to be able to estimate the properties by means of theoretical work. In the present work, dielectric constant and loss for polypropylene-meso-erythritol compounds were studied. The experimental results were compared to the theoretically assessed properties.The compounds were prepared in three different concentrations. The obtained samples were pressed to plates which were characterized by dielectric responsemeasurements. The dielectric constants were also assessed using Maxwell-Garnett estimation and molecular dynamics simulations. For the later, bothatomistic model and a more coarse multiscale model were used. The Maxwell-Garnett equation gave a good estimation of the dielectric constant level whereas with the molecular dynamics simulations the obtained dielectric constant were in exact accordance to the measured values. With the molecular dynamics simulation, also the loss could be estimated. As expected, the atomistic model gave better correlation to the measured loss levels than the multi-scale model.

High Permeability of Z-Type Ferrite Sheets Directional Array

Z-type ferrite sheets were prepared by chemical precipitation method to investigate influences of directional arrays from the Z-type ferrite sheets on magnetic properties. The permeability of the ferrite directional arrays was obviously improved in the specific direction. Assuming that the intrinsic permeability of Z-type ferrite was existed, the magnetic permeability in array was calculated by the Maxwell-Garnett equation of effective media theory. The reason for the large difference between the theoretical calculation and measured value was also discussed.

A metal-ceramic coaxial cable Fabry-Pérot microwave interferometer for monitoring fluid dielectric constant

A metal-ceramic coaxial cable Fabry-Pérot interferometer (MCCC-FPI) has been developed as a new microwave sensor and demonstrated for fast and reliably measuring and continuously monitoring dielectric constants for pure and mixed liquids. The sensor only requires a simple reference scan of the interferogram for the FPI with its sensing chamber filled with air or under vacuum to determine the actual inter-reflector length. The sensor is validated by measuring room temperature dielectric constant (εr) at high frequencies around 1.4–4.7GHz for three vegetable oils (corn, sesame, and olive), the synthetic Mobil®-1 engine oil, and mixtures containing sesame oil and water. The sensor has been also successfully demonstrated for determining εr values for the Mobil-1 oil at various temperatures and for the well-dispersed sesame oil-water mixtures of different compositions. The Bottcher’s model of effective medium theory is shown to be better suited for predicting the εr of the sesame oil-water mixture than the Maxwell-Garnett and Bruggeman equations of spherical solutions.

Perovskite-spinel composite approach to modify room temperature structural, magnetic and dielectric behavior of BiFeO3

In the present attempt, we report modified features of structural, dielectric, magnetic and ferroelectric behaviour of BiFeO3 (BFO) by perovskite-spinel composite approach. ZnFe2O4 (ZFO) is used as spinel phase. The structural measurement of composite show anisotropically compression in the BiFeO3 lattice with ZFO compositions and stimulates the variation in bond length, bond angle, tilting angle, electron density and resultant polarization. This affects on magnetic and dielectric behaviour of BFO. Room temperature magnetic measurement revealed enhancement of magnetization of BFO in composite, attributed to spin restructuring due to change in magnetic anisotropy, exchange energy and stress energy at interface with ZFO composition. There is around 7 times enhancement in magnetization as compared to pure BFO phase. Dielectric profile of composites shows decrease in dielectric constant as well as dielectric loss as compared to single phase BFO. P-E loop exhibits leaky ferroelectric behaviour of composite system with drop down in leakage current by 2 order of magnitude than pure BFO phase. Magnetic contributions of individual phases in composite are determined by Vegard Law while dielectric contributions are modelled by Maxwell-Garnett (MG) equation. The present work demonstrates that BFO-ZFO: perovskite-spinel composite approach to modify magnetic, dielectric and ferroelectric behaviour and to facilitate BFO as room temperature multiferroic system.

Improvements in thermo-mechanical and rheological properties of SiO2/epoxy composites using different types of SiO2

Single-size 400 nm-SiO2 and multi-size 1 and 5 μm-SiO2 were used as fillers in epoxy matrix. The fillers with the larger particle size and multi-size SiO2 particles mixing is beneficial to lower the viscosity and increase the filler loading. Among the composites, the 60 wt% 5 μm-SiO2 epoxy composite has the best properties with both low coefficients of thermal expansion (CTE) of 28.8 ppm/°C and low viscosity of ~50 Pa s, which shows its capability to achieve the required low CTE and viscosity values in the electronic packaging. Different theoretical proposals were used to estimate the CTE. Maxwell–Garnett equation fits the experimental data well. In addition, the mixture law and Bruggeman effective medium theory offer the upper and lower limits to the CTE.

Characteristic investigation of scanning surface plasmon microscopy for nucleotide functionalized nanoarray.

A calculation based on surface plasmon coupling condition and Maxwell-Garnett equation was performed for predicting the coupling angle shift and thin film thickness in scanning surface plasmon microscopy (SSPM). The refractive index sensitivity and lateral resolution of an SSPM system was also investigated. The limit of detection of angle shift was 0.01°, the limit of quantification of angle shift was 0.03°, and the sensitivity was around 0.12° shift per nm ZnO film when the film thickness was less than 22.6 nm. Two partially connected Au nano-discs with a center-to-center distance of 1.1 μm could be identified as two peaks. The system was applied to image nanostructure defects and a virus-probe functionalized nanoarray. We expect the potential application in nanobiosensors with further optimization in the future.

Influence of the surface roughness and oxide surface layer onto Si optical constants measured by the ellipsometry technique

Si crystal surface after chemical etching was studied using ellipsometry, atomic force microscopy and scanning tunneling microscopy. The ellipsometric parameters as functions of light incidence angles at two light wavelengths 546.1 and 296.7 nm were measured. The calculations based on equations for the plane surface have shown that the refractive index and absorption coefficient values are different from those determined earlier. Two models for surface layers were developed. After etching, the upper layer contains chemical compounds and the lower layer characterizes the sample roughness. By applying Airy's formula to ellipsometric data, optical constants and thicknesses of the layers were obtained. The calculated values of bulk Si optical constants wholly correspond to the data from literature. The calculated thickness of the lower layer is similar to that obtained through scanning tunneling microscopy measurements. Calculations based on Maxwell-Garnett and Bruggeman equations were performed to determine the content of silicon particles within the lower rough layer.

Study of magnetic, dielectric and magnetodielectric properties of BaTiO3/Fe3O4 core/shell nanocomposite

Multiferroic systems fashioned by involvement of a ferroelectric phase and a ferromagnetic phase have received significant attention because of their wide possibilities for tailoring properties. However, many interrogations persist about how the structure and chemistry of interface mediates magnetodielectric activities. In this study, we have explored the magnetic, dielectric and magnetodielectric behavior of BaTiO3/Fe3O4 core/shell nanocomposite synthesized by combined co-precipitation cum sonochemical method. The phase formation of the core/shell naonocomposite was confirmed independently from X-ray diffraction and selected area electron diffraction studies. The microstructure of the sample was studied by transmission electron microscopy and High resolution TEM revealing a good mixing of two phases in the form of core (BaTiO3)/shell (Fe3O4). Magnetic property of the sample was investigated using a vibrating sample magnetometer (VSM) at room temperature. The magnetic study reveals that the synthesized core/shell nanocompositeis ferromagnetic with saturation magnetization of ~58 emu/g. The dielectric constant of the core/shell nanocomposite, measured as a function of temperature, at frequencies 1, 10, 100, 500 and 1 MHz combines almost the characteristics of BaTiO3 and Fe3O4 in accordance with the Maxwell–Garnett equation. However, near 125 K a clear hump is observed probably due to characteristic Verwey transition (TV) in Fe3O4. The dielectric constant also shows dispersion behavior with increasing frequency due to Maxwell–Wagner interfacial polarization. Furthermore, the shrinkagein dielectric constant (at 20 K) on the application of 1 T external magnetic field depicts the possible coupling between the dielectric (BaTiO3) and the magnetic (Fe3O4) phases of BaTiO3/Fe3O4 core/shell nanocomposite.

Atomistic understanding of diffusion kinetics in nanocrystals from molecular dynamics simulations

Understanding the grain size effect on diffusion in nanocrystals has been hampered by the difficulty of measuring diffusion directly in experiments. Here large-scale atomistic modeling is applied to understand the diffusion kinetics in nanocrystals. Enhanced short-circuit diffusivity is revealed to be controlled by the rule of mixtures for grain-boundary diffusion and lattice diffusion, which can be accurately described by the Maxwell-Garnett equation instead of the commonly thought Hart equation, and the thermodynamics of pure grain-boundary self-diffusion is not remarkably affected by varying grain size. Experimentally comparable Arrhenius parameters with atomic detail validate our results. We also propose a free-volume diffusion mechanism considering negative activation entropy and small activation volume. These help provide a fundamental understanding of how the activation parameters depend on size and the structure-property relationship of nanostructured materials from a physical viewpoint.

Effect of inclusions' distribution on microwave absorbing properties of composites

Effect of inclusions' spatial distributions on the permeability and permittivity of composites is studied using the generalized Maxwell-Garnett equations. The result indicates that inclusions' orientation distribution can increase the longitudinal electromagnetic parameters. For inclusions' random and orientation distribution, single and three-layer absorbers are designed and optimized using genetic algorithm. The result shows that under a given absorbing requirement, absorber with inclusions' orientation distribution is lighter and thinner than absorber with inclusions' random distribution.

Microwave properties of double layer absorber reinforced with carbon fibre powders

Epoxy resin based double layer absorbing coatings were prepared, employing carbonyl iron and carbon black as original absorbents in the matching layer and absorbing layer respectively. Carbon fibre powders (CFPs) were introduced as additional absorbent in the two layers. The absorbers were tested to investigate their absorbing performances, including SEM, electromagnetic parameters and reflection loss. The advantage of adding CFP to the absorbing layer in improving the microwave performance was more obvious than that to matching layer. Results showed that an optimal content of CFP/carbon black/epoxy resin in the absorbing layer was 0·25∶0·25∶1 with a bandwidth (reflection loss <−10 dB) of 4·5 GHz. The absorption peak shifted to lower frequency when the content of CFP increased, as explained by Maxwell–Garnett equation and quarter wavelength resonance equation. The extra addition of CFP to the coatings was verified to be effective in controlling the wave absorbing properties.

Microwave Debye relaxation analysis of dissolved proteins: Towards free-solution biosensing

Aqueous solutions of a variety of proteins at different concentrations are examined through microwave spectroscopy and compared to sodium chloride and polystyrene nanospheres. The complex permittivity is analysed in terms of the Debye model and the Stokes-Einstein-Debye relation in conjunction with the Maxwell-Garnett equation. According to Einstein’s classical theory of viscosity with Brenner’s adaptation [H. Brenner, Chem. Eng. Sci. 27, 1069 (1972)] for arbitrary solute shapes, the ratio of the alterations of static permittivity and relaxation time of low concentration solutions is found to be independent of concentration and determined by the molecular shape. Our results represent a route towards free-solution identification through molecular finger-printing.