Influence of Scatterer's Geometry on Power-Law Formula in Random Mixing Composites

Zhou, Peiheng; Deng, Longjiang; Wu, Bae‐Ian; Kong, Jin Au

doi:10.2528/pier08081705

Cited by 16 publications

(11 citation statements)

References 14 publications

(15 reference statements)

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“…There have been several attempts to account analytically for random shape and position of small inclusions in a medium and derive the effective properties of the composite media,18 with variable rates of success. Comparison and description of these effective medium models is a separate active research topic19–20 and beyond the scope of this paper. Since, empirically, most of these models, none being exact, result in similar predictions of effective medium properties, it is sufficient to perform the entire analysis based on a single model.…”

Section: Approachmentioning

confidence: 99%

Optical Response of Magnetic Fluorescent Microspheres Used for Force Spectroscopy in the Evanescent Field

et al. 2010

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Force spectroscopy based on magnetic tweezers is a powerful technique to manipulate single biomolecules and study their interactions. The resolution in a magnetic probe displacement, however, needs to be commensurate with molecular sizes. To achieve the desirable sensitivity in tracking displacements of the magnetic probe, some recent approaches have combined magnetic tweezers with total internal reflection fluorescence microscopy. In this situation, a typical force probe is a polymer microsphere containing two types of optically active components -a pure absorber (magnetic nanoparticles for providing the pulling force) and a luminophore (semiconducting nanoparticles or organic dyes for fluorescent imaging). In order to fully assess the system's capability for tracking the position of the force probe with sub-nanometer accuracy, we developed a body-of-revolution formulation of the method of auxiliary sources (BOR-MAS) to simulate absorption, scattering, and fluorescence of microscopic spheres in an evanescent electromagnetic field. The theoretical formulation uses the axial symmetry of the system to reduce the dimensionality of the modeling problem and produces excellent agreement with the reported experimental data on forward scattering intensity. Using the BOR-MAS numerical model, we investigated the probe detection sensitivity for a high numerical aperture objective. The analysis of both backscattering and fluorescence observation modes shows that the total intensity of the bead image decays exponentially with the distance from the surface (or the length of a biomolecule). Our investigations demonstrate that the decay lengths of observable optical power are smaller than the penetration depth of the unperturbed excitation evanescent wave. In addition, our numerical modeling results illustrate that the expected sensitivity for the decay length changes with the incident angle, tracking the theoretical penetration depth for a two-media model, and is sensitive to the bead size. The BOR-MAS methodology developed in this work for near field modeling of bead tracking experiments fully describes the fundamental photonic response of microscopic BOR probes at the sub-wavelength level and can be used for future improvements in the design of these probes or in the setup of bead tracking experiments.

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Section: Approachmentioning

confidence: 99%

Optical Response of Magnetic Fluorescent Microspheres Used for Force Spectroscopy in the Evanescent Field

et al. 2010

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“…All these equations along with the other empirical equations of (6) to (8) will be studied. Some of the above rules have been studied in recent years [3,[7][8][9][10]. Unfortunately, they have been studied without knowledge about their theoretical errors.…”

Section: Mixture Equationsmentioning

confidence: 99%

“…One of the most well known representative equations to simulated dielectric constants of composites containing the fillers are the exponential mixture rules [1][2][3][4][5][6][7][8][9][10][11][12][13][14],…”

Section: Mixture Equationsmentioning

confidence: 99%

Microwave Measurements of Dielectric Constants by Exponential and Logarithmic Mixture Equations

Sheen¹,

Hong²,

Su³

et al. 2010

PIER

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Abstract-This article reports on a study of the dielectric constants of ceramic dispersions in the polyethylene matrix at microwave frequency. The exponential and logarithmic mixture rules are studied in three ceramic powders of fillers with dielectric constants 10, 20, and 36, respectively. The experimental values of the dielectric constants of the mixtures are compared to those obtained by using different mixing laws. The mixing rules are also adopted to calculate the dielectric constants of pure ceramics from the measured dielectric constants of composites with various concentrations. The theories on errors of calculations are studied. The most adequate mixture equation for measuring the dielectric constants of pure ceramics is suggested.

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“…When α = 1, the inclusions have no depolarisation and we obtain the arithmetic mean of the dielectric functions [23].…”

Section: Effective Dielectric Functionsmentioning

confidence: 99%

Near Field Heat Transfer between Random Composite Materials: Applications and Limitations

Santiago

Esquivel‐Sirvent

2016

Zeitschrift Für Naturforschung A

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Abstract:We present a theoretical study of the limits and bounds of using effective medium approximations in the calculation of the near field radiative heat transfer between a composite system made of Au nanoparticles in a SiC host and an homogeneous SiC slab. The effective dielectric function of the composite slab is calculated using three different approximations: Maxwell-Garnett, Bruggeman, and Looyenga's. In addition, we considered an empirical fit to the effective dielectric function by Grundquist and Hunderi. We show that the calculated value of the heat flux in the near field is dependent on the model, and the difference in the effective dielectric function is larger around the plasmonic response of the Au nanoparticles. This, in turn, accounts for the difference in the near field radiative heat flux. For all values of filling fractions, the Looyenga approximation gives a lower bound for the heat flux.

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Influence of Scatterer's Geometry on Power-Law Formula in Random Mixing Composites

Cited by 16 publications

References 14 publications

Optical Response of Magnetic Fluorescent Microspheres Used for Force Spectroscopy in the Evanescent Field

Optical Response of Magnetic Fluorescent Microspheres Used for Force Spectroscopy in the Evanescent Field

Microwave Measurements of Dielectric Constants by Exponential and Logarithmic Mixture Equations

Near Field Heat Transfer between Random Composite Materials: Applications and Limitations

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