Maxwell-Garnett Effective Medium Theory Research Articles

Photoelectric-coupled multilayer smart glass synergistically regulated with doped nanoparticles of GaAs and IST phase change layers

Windows are the main part of the building energy exchange. Most of the solar energy that passes through the windows is reflected or converted into heat loss, which causes a great waste of energy. To improve the energy utilization, this work presents the design of a multilayer glass with a GaAs layer doped by nanoparticles and an IST (In3SbTe2) phase change layer. The dielectric function of the doped layer is obtained by the Maxwell-Garnett effective medium theory. The transmittance and the photoelectric conversion efficiency are calculated through the transfer matrix method. With the genetic algorithm, the structure parameters are optimized to achieve the high values of both average transmittance in human-eye response band and photoelectric conversion energy. The average transmittance of the human eye response band for the structure containing only GaAs doped layer reaches 0.5–0.6, and the average photovoltaic conversion efficiency is above 0.2. After adding the IST phase change layer, the difference of ranges of the spectral regulation between the two phases in the metal nanoparticle doped structure can reach more than 0.25. The light transmission regulation is realized by active phase change. This work provides an optimization-based analysis approach and a possible design of the multilayer smart glass.

Extinction and attenuation by voids in absorbing host media.

Extinction and attenuation by particles in an absorbing host have suffered a long-lasting controversy, which has impeded the physical insights on the radiative transfer in the voids dispersed composite. In this paper, we outline the existing extinction definitions, including an equivalence theorem neglecting the host absorption, the near-field analytical definition neglecting the far-field effects, and the operational way which simulates the actual detector readings. It is shown that, under the independent scattering approximation, the generalized operational definition is equivalent to a recent effective medium method according to the rigorous theory of multiple scattering. Using this generalized extinction, we show the important influences of the host absorption on the void extinction. Specifically, at the void resonance, the extinction cross sections of the small voids can be positive, zero, and even negative, which is regulated quantitively by host absorption. Considering the voids in SiC or Ag, the intriguing properties are verified through the attenuation coefficient calculated by the Maxwell-Garnett effective medium theory. In contrast, the equivalent theorem cannot describe any void resonance structures in the absorbing media. Also, the near-field definition fails to generate negative extinction and cannot thus describe the diminished total absorption by the voids. Our results might provide a better understanding of complex scattering theory in absorbing media.

Enhanced magneto-optical properties of Fe3O4@Au nanoparticles and its reverse core-shell nanostructure embedded in host matrix SiO2

We studied the effect of electric and magnetic polarizability of Fe3O4@Au and the reverse structure Au@Fe3O4 core-shell spherical nanostructures embedded in SiO2. Employing electrostatic approximation and Maxwell-Garnett effective medium theory, we evaluate the electric and magnetic polarizability, the refractive index and absorbance as a function of radiation energy. The modified Drude-Lorentz form and Lorentz model used to evaluate ϵ(ω) and μ(ω), respectively. For fixefd r2 = 30 nm, β = 0.875, εh = 3.9 and f = 0.001 maximum absorbance obtained at E = 2.742 eV for Au@Fe3O4 core-shell and at E = 2.937 eV for the reverse structure with β = 0.578. The ratio of the maximum absorbance peak of Au@Fe3O4 core-shell to Fe3O4@Au core-shell gives 3.5. Both graphs of n2 and absorbance possess three sets of peaks. All sets of resonance peaks of Fe3O4@Au found in the visible region. For the revers structure the first two sets of resonance peaks found in the visible region and the third set of resonance peaks in UV region. The peaks arise due to the coupling between the surface plasmon of the gold metal with Fe3O4∕SiO2 interfaces and the interaction of incident radiation with magnetic dipole moment of the magnetic semiconducting nanoparticles. The findings may be used in applications that require the combined plasmonic and magnetic effects such as drug delivery.

Simulation of Fe2O3/Au@MoS2 plasmonic core/shell@shell nanocomposites: Optical properties and photothermal application

The plasmonic and magneto-plasmonic nanocomposites are multi-functional structures that are applicable to medical applications such as tumor therapy, diagnosis, and biosensors. Here, the simulation of the optical and photothermal properties of plasmonic nanocomposites has been done. The spherical core@shell and core/shell@shell nanocomposites have been modeled using the generalized Mie theory. Au and Fe2O3 have been used as plasmonic and magnetic structures because of their bio-compatibility and then the role of MoS2 shell has been examined. The results show that these structures are very effective in photothermal therapy since their localized surfaced plasmon resonance is situated in the near-infrared region of electromagnetic waves. Among the simulated structures, Fe2O3@Au shows the best plasmonic behavior and absorption efficiency enhanced about 7 when the core radius is 20 nm, and the shell thickness and wavelength of incident light are between 5 and 10 nm and 700–800 nm, respectively. Maxwell-Garnett's effective medium theory has been used to calculate the effective permittivity of nanocomposites as well as the simulation of the temperature increase under laser radiation. The temperature enhancement of single nanocomposites shows very promising results. The single Fe2O3/Au@MoS2core/shell@shell nanocomposite illustrates the highest performance in temperature increase with 10−3K.

Maxwell-Garnett permittivity optimized micro-porous PVDF/PMMA blend for near unity thermal emission through the atmospheric window

Owing to excellent solar reflectivity and sky window emissivity, disordered heterogenous materials, including filler-abundant matrices, paints, and coatings, as well as foam-like, fiber-stacked and composite porous structures, form a major class for efficient passive radiative cooling. Contrary to well-established empirical understanding, this work offers a generalized analytical overview of their macroscopic thermo-optical properties from the microscopic electromagnetic perspective of Maxwell-Garnett effective medium theory. With the family of micro-porous poly(vinylidene-fluoride)/poly(methyl-methacrylate) blends as a representative example, procedures for tailoring mid-infrared spectral emissivity via effective permittivity are outlined. Theoretical framework and design scheme are validated by finite difference time domain simulation and Fourier transform infrared spectrometry. It is shown that poly(vinylidene-fluoride) and poly(methyl-methacrylate) form a pair of complementary constitutive materials for near unity thermal emission through the atmospheric window. Optimized binary polymeric blend, prepared by spray-coating method, features a window emissivity of 98% and realizes nocturnal radiative cooling with a temperature reduction of 6.8 °C and a cooling power of 94 W/m 2 in an outdoor field investigation. It can serve as a promising bifunctional material for simultaneous radiative heat dissipation and capacitive energy storage, which meets the demand for nocturnal, radiative cooling aided thermoelectricity generation and storage potential. • Maxwell-Garnett effective medium theory is employed for disordered heterogeneous radiative cooling materials design. • Thermal-radiative properties of PVDF/PMMA blends are optimized. • Temperature reduction of 6.8 °C and cooling power of 94 W/m2 are realized in nocturnal field investigation.

Complementary Vanadium Dioxide Metamaterial with Enhanced Modulation Amplitude at Terahertz Frequencies

One route to create tunable metamaterials is through integration with ``on-demand'' dynamic quantum materials, such as vanadium dioxide (${\mathrm{VO}}_{2}$). This enables modalities to create high-performance devices for historically challenging applications. Indeed, dynamic materials have often been integrated with metamaterials to imbue artificial structures with some degree of tunability. Conversely, metamaterials can be used to enhance and extend the natural tuning range of dynamic materials. Utilizing a complementary split-ring resonator array deposited on a ${\mathrm{VO}}_{2}$ film, we demonstrate enhanced terahertz transmission modulation upon traversing the insulator-to-metal transition (IMT) at approximately $340$ K. Our complementary metamaterial increases the modulation amplitude of the original ${\mathrm{VO}}_{2}$ film from 0.42 to 0.68 at 0.47 THz upon crossing the IMT, corresponding to an enhancement of 62%. Moreover, temperature-dependent transmission measurements reveal a significant redshift of the resonant frequency in a narrow temperature range where phase coexistence is known to occur. Neither Maxwell-Garnett nor Bruggeman effective medium theory adequately describes the observed frequency shift and amplitude decrease. However, a Drude model incorporating a significant increase of the effective permittivity does describe the experimentally observed redshift. Our results highlight that symbiotic integration of metamaterial arrays with quantum materials provides a powerful approach to engineer emergent functionality.

Onset of a superconductor-insulator transition in an ultrathin NbN film under in-plane magnetic field studied by terahertz spectroscopy

Optical conductivity of a moderately disordered superconducting NbN film was investigated by terahertz time-domain spectroscopy in external magnetic field applied along the film plane. The film thickness of about 5 nm was comparable with the coherence length, so vortices should not form. This was confirmed by the fact that no marked difference between the spectra with terahertz electric field set perpendicular and parallel to the external magnetic field was observed. Simultaneous use of Maxwell-Garnett effective medium theory and the model of optical conductivity by Herman and Hlubina proved to correctly reproduce the terahertz spectra obtained experimentally in a magnetic field of up to 7 T. This let us conclude that the magnetic field tends to suppress the superconductivity, resulting in an inhomogeneous state where superconducting domains are enclosed within a normal-state matrix. The scattering rate due to pair-breaking effects was found to linearly increase with magnetic field.

Validity of the effective medium theory for modeling near-field thermal emission by nanowire arrays

Nanowire arrays are promising man-made materials for tuning the spectrum and the magnitude of near-field thermal radiation. Near-field radiative properties of nanowire arrays are often studied using the effective medium theory (EMT). In this paper, we inspect the validity of the Maxwell-Garnett (MG) and Bruggeman (BR) EMTs for predicting near-field thermal emission by quartz and indium tin oxide (ITO) nanowire arrays. The near-field energy density predicted using the EMTs is compared with numerical simulations obtained using the thermal discrete dipole approximation. For quartz nanowire arrays, which support localized surface phonons in the infrared region, neither MG nor BR EMT can accurately predict the spectrum and the magnitude of near-field thermal emission even at distances, zo, greater than the array pitch, L over π. Based on the performed simulations, the EMT agrees the best with the T-DDA when 1<Lzo<π. It is also shown that MG EMT is slightly more consistent with numerical simulations than the BR EMT. For the ITO array, which does not support localized surface plasmons in the infrared region, the MG EMT provides an acceptable estimations of near-field thermal radiation. Finally, it is observed that near-field emission can vary by a factor of two in lateral directions which cannot be captured in the EMT.

Modulated 3D light absorption profile in GaN nanorod arrays

The depth dependent UV-light absorption profile of GaN nanorods with different lattice arrays and filling factors was studied using finite-difference time-domain (FDTD) methods. By comparing to the results from Lambert-Beer's law with Maxwell-Garnett effective medium theory, we identified the quantitative contribution from nano-scattering effect on the light absorption in the nanorod arrays. The FDTD study of graphical 3D profile of light absorption and electric field intensity was parallelly conducted to investigate the origin of the nano-scattering. We found that the coupled electric field in the gap regions led to the larger absorption cross-section of the nanorod arrays, which is attributed to the distorted depth profile of the light absorption.

Glycine functionalized boron nitride nanosheets with improved dispersibility and enhanced interaction with matrix for thermal composites

Hexagonal boron nitride nanosheets (BNNS) have been widely investigated as promising fillers for thermal composites because of their high thermal conductivity and electrical insulation, which avoid the short circuit risk effectively when applied in electronics. However, the poor dispersibility and weak interaction with matrix have hindered the further improvement of BNNS based thermal composites. Here, we propose a simple and green amino acid-assisted ball milling exfoliation process for highly hydrophilic glycine (NH2-CH2-COOH)-functionalized BNNS (BNNS-Gly) to improve their dispersion and reduce the thermal interface resistance between fillers and matrix. Three different types of thermal management materials have been prepared by dispersing BNNS-Gly into water, epoxy resin, and cellulose respectively, and their thermal properties have been investigated. As a result, the BNNS-Gly water nanofluid exhibits a 110% increment in thermal conductivity at 1.6 vol% loading compared with pure water. For BNNS-Gly/Epoxy composite, an enhancement of 109% of thermal conductivity compared with pure BNNS/Epoxy is achieved. According to the calculation of the Maxwell-Garnett effective medium theory (EMT) model, the thermal interface resistance between BNNS-Gly and epoxy is reduced by 62%. Besides, the thermal conductivity of BNNS-Gly/cellulose nanofiber (CNF) film reaches up to 16.2 W/mK at 70 wt% loading, which is 1.8-fold of that for BNNS/CNF. In summary, BNNS-Gly fabricated by this work show great advantages in thermal properties compared with widely-used pure BNNS based composites for improved dispersibility and enhanced interaction with matrix.

Near-field radiative heat transfer between nanowire-based dual uniaxial magneto-dielectric metamaterials

Over past several years, much attention has been paid on near-field radiation with super-Planckian heat flux due to resonant coupling of surface polaritons and non-resonant hyperbolic modes but mainly with non-magnetic materials. With nanowire-based magneto-dielectric metamaterials, this work theoretically investigates the near-field radiative heat transfer associated with both uniaxial magnetic and electric responses. Maxwell–Garnett effective medium theory is used to obtain the dual uniaxial effective permeability and permittivity of the magneto-dielectric metamaterials. With the fluctuational electrodynamics, multiple resonant and non-resonant modes associated with both magnetic and electric responses that spectrally enhance the radiative heat transfer, such as magnetic and electric hyperbolic modes, magnetic and electric surface polaritons, mu- and epsilon-near-pole modes, are identified and elucidated at different wave polarizations. Effects of filling ratio, magnetic and electric scattering rates, and vacuum gap distance are also studied, and it is found that the spectral and total heat fluxes of s-polarized waves, which are usually neglected for non-magnetic materials, are much enhanced and comparable with that of p-polarized waves. The results here will deepen the fundamental understanding in magneto-dielectric metamaterials and facilitate their applications in the area of near-field thermal radiation.

Multipolar Resonances with Designer Tunability Using VO2 Phase-Change Materials

Subwavelength nanoparticles can support electromagnetic resonances with distinct features depending on their size, shape, and nature. For example, electric and magnetic Mie resonances occur in dielectric particles, while plasmonic resonances appear in metals. Here, we experimentally demonstrate that the multipolar resonances hosted by ${\mathrm{VO}}_{2}$ nanocrystals can be dynamically tuned and switched thanks to the insulator-to-metal transition of ${\mathrm{VO}}_{2}$. Using both Mie theory and Maxwell-Garnett effective-medium theory, we retrieve the complex refractive index of the effective medium composed of a slab of ${\mathrm{VO}}_{2}$ nanospheres embedded in ${\mathrm{Si}\mathrm{O}}_{2}$ and show that such a resulting metamaterial presents distinct optical tunability compared to unpatterned ${\mathrm{VO}}_{2}$. We further show that this approach provides a new degree of freedom to design low-loss phase-change metamaterials with record large figure of merit ($\mathrm{\ensuremath{\Delta}}n/\mathrm{\ensuremath{\Delta}}k$) and designer optical tunability.

High-sensitivity identification of aflatoxin B1 and B2 using terahertz time-domain spectroscopy and metamaterial-based terahertz biosensor

Aflatoxin B1 and B2 are extremely toxic to humans and commonly found in agricultural and food products. Thus, rapid and accurate detection and identification of these substances is essential to prevent human and animal health problems due to their consumption. Here, we present a metamaterial-based terahertz biosensor that has the potential for high-sensitivity, quantitative identification of aflatoxin B1 and B2 in extremely small amounts. By combining with conventional terahertz time-domain spectroscopy and the Maxwell-Garnett effective medium theory, we directly obtained accurate information of the refractive index, absorption coefficient, and dielectric function of these aflatoxins, which are essential parameters to understand their physical properties for their identification. Furthermore, the resonant frequency of the proposed biosensor was in a frequency range wherein the largest difference between the two aflatoxins was observed. In addition, the sensing of aflatoxin B1 and B2 was demonstrated as a function of content, thickness and dielectric constant by the THz biosensor and finite-element simulation. Consequently, a qualitative and quantitative identification of trace aflatoxin B1 and B2 without label was achieved.

The improved performance of BHJ organic solar cells by random dispersed metal nanoparticles through the active layer

In this paper, the performance of bulk heterojunction (BHJ) organic solar cells (OSCs) in the presence of random dispersed Ag nanoparticles (NPs) into the active layer is investigated. By the well-known Maxwell-Garnett effective medium theory, we have analyzed the optical absorption of P3HT:PCBM and PCDTBT:PCBM photoactive blends when spherical Ag NPs are randomly embedded in them. The photocurrent enhancement of OSCs based on the blend:AgNP composites has been examined by an analytical drift-diffusion method. Our theoretical analysis demonstrates a considerable enhancement in the optical absorption of the blends with Ag NPs resulted in the power conversion efficiency (PCE) improvement of the devices up to 65.6% in comparison with the reference blends. In addition, the spectrally correlation of simulated external quantum efficiency (EQE) and the absorption coefficient enhancements proves the influence of localized surface plasmon resonance (LSPR) of the Ag NPs in boosting the performance of the OSC devices.

Studying corrosion of silver thin film by surface plasmon resonance technique

A novel strategy is proposed by using surface plasmon resonance technique to investigate the corrosion process of silver thin film within 100 nm thickness exposed to laboratory air. Specifically, we continuously test surface plasmon resonance curves of silver thin film for 40 days and calculate its permittivity and thickness. Measurements of energy dispersive spectrometer indicate that there are silver sulfide formations on the film surface in the corrosion process. By using Maxwell–Garnett effective medium theory, the volume fraction of silver sulfide was confirmed in the silver/silver sulfide composites film. The results reveal that the concentration of silver sulfide in the film sample increases exponentially during the corrosion process and increases rapidly in the initial stage.

Determination of complex dielectric function of CH3NH3PbBr3 perovskite cubic colloidal quantum dots by modified iterative matrix inversion method.

Recent advances in lead halide perovskite quantum dots appeal with their potential in various optoelectronic devices such as photovoltaics, photodetectors, light-emitting diodes (LEDs) and lasers. However, lack of information on the intrinsic optical properties of lead halide perovskite quantum dots (QDs) lags the progress in device performances and further development in various applications. In this letter, the complex dielectric function of CH3NH3PbBr3 perovskite cubic colloidal QDs was determined from the UV-Vis absorption by using a modified iterative matrix inversion (IMI) method. The modified IMI method takes into account the dilute solution with cubic inclusions, while the conventional method only considers spherical or elliptical inclusions by Maxwell-Garnett (MG) effective medium theory. In addition, singly subtractive Kramer Kronig (SSKK) relations have also been considered to compensate for possible errors arising from the finite wavelength range of the experimental absorption data.

Size dependent optical properties of ZnO@Ag core/shell nanostructures

In this paper, we studied the effect of size and thickness variation on the optical properties of a system that consists of spherical ZnO@Ag core/shell composite nanostructures embedded in a dielectric host matrix. The effective dielectric function, polarizability, refractive index, and absorbance of the composite nanostructures are determined using the Maxwell-Garnett effective medium theory within the framework of the electrostatic approximation. The numerical simulations using nanoinclusions of radii 20 nm show interesting behavior in the optical responses of the ensemble. In particular, it is shown that for different values of metal fraction and filling factor, the polarizability, refractive index, and optical absorbance of the ensemble exhibit two sets of resonance peaks in the UV (around 300 nm) and visible (between 400 and 640 nm) spectral regions. These peaks are attributed to the surface plasmon resonance of silver at the ZnO/Ag and Ag/host-matrix interface. Moreover, when the Ag shell thickness is increased, the observed resonance peaks are enhanced; accompanied with slight red shifts in the UV and blue shifts in the visible regions. The results obtained may be used in various applications such as sensors and nano-optoelectronics devices in optimizing material parameters to the ‘desired’ values.

Limits of the Effective Medium Theory in Particle Amplified Surface Plasmon Resonance Spectroscopy Biosensors

The resonant wave modes in monomodal and multimodal planar Surface Plasmon Resonance (SPR) sensors and their response to a bidimensional array of gold nanoparticles (AuNPs) are analyzed both theoretically and experimentally, to investigate the parameters that rule the correct nanoparticle counting in the emerging metal nanoparticle-amplified surface plasmon resonance (PA-SPR) spectroscopy. With numerical simulations based on the Finite Element Method (FEM), we evaluate the error performed in the determination of the surface density of nanoparticles σ when the Maxwell-Garnett effective medium theory is used for fast data processing of the SPR reflectivity curves upon nanoparticle detection. The deviation increases directly with the manifestations of non-negligible scattering cross-section of the single nanoparticle, dipole-dipole interactions between adjacent AuNPs and dipolar interactions with the metal substrate. Near field simulations show clearly the set-up of dipolar interactions when the dielectric thickness is smaller than 10 nm and confirm that the anomalous dispersion usually observed experimentally is due to the failure of the effective medium theories. Using citrate stabilized AuNPs with a nominal diameter of about 15 nm, we demonstrate experimentally that Dielectric Loaded Waveguides (DLWGs) can be used as accurate nanocounters in the range of surface density between 20 and 200 NP/µm2, opening the way to the use of PA-SPR spectroscopy on systems mimicking the physiological cell membranes on SiO2 supports.

An aqueous-only, green route to exfoliate boron nitride for preparation of high thermal conductive boron nitride nanosheet/cellulose nanofiber flexible film

With the rapid development of electronic device, thermal management material is currently in great demand. Therefore, to design material of efficient thermal management is of high significance. In this work, we report a green route that using only water exfoliate boron nitride (BN) powder and obtain hydroxylate boron nitride nanosheets (BNNS-OH) aqueous dispersion. The BNNS-OH as high thermally conductive nanofillers composited with cellulose nanofiber (CNF) is prepared a flexible film which has high thermal conductivity, superior mechanical properties and good thermal stability. In BNNS-OH/CNF film, BNNS-OH and CNF are stacked layer-by-layer to form a natural nacre structure, where CNF acted as the mortar filled in the interlayer space. The in-plane thermal conductivity of the 25 wt%BNNS-OH/CNF film is 22.67 W m−1 K−1, corresponding to thermal boundary resistance is 3.26 × 10−6 m2 kW−1 calculated by the Maxwell-Garnett effective medium theory (EMT) which is lower than that by previously reported methods. We demonstrate the potential usefulness of BNNS-OH/CNF film in electronic device-cooling application.

On the piezoresistive behavior of carbon fibers - Cantilever-based testing method and Maxwell-Garnett effective medium theory modeling

A good understanding of the piezoresistive behavior of carbon fiber is highly valuable in studying the processing-structure-property relationship of this very important engineering material. Up-to-date, there is still a lack of agreement on the physical origin of the unique modulus-dependent piezoresistivity for carbon fibers. In the present work, an experimental and theoretical modeling combined approach was taken to attack this long outstanding issue. A cantilever testing method was developed which allows for the evaluation of the piezoresistive behavior of a single carbon fiber filament under axial tension and compression mode. It was found that the tensile and compressive piezoresistive behavior showed antisymmetric characteristics. This supports the concept that the orientation of the basic structural units (BSUs) is responsible for the piezoresistivity of carbon fibers. Such an argument was further augmented by theoretical modeling of the carbon fiber piezoresistivity based on a Maxwell Garnett theory approach. The new piezoresistivity model identifies the critical role of the compound effect of the BSU orientation and its volume fraction in dictating the piezoresistive behavior of carbon fibers. With consideration of this compound effect, the modulus-dependent piezoresistivity data of carbon fibers reported in the past few decades can now be well explained.