Complex permittivity of a dielectric mixture: corrected version of Lichtenecker's logarithmic law of mixing

Neelakantaswamy, P. S.; Turkman, R.I.; Sarkar, Tapan K.

doi:10.1049/el:19850192

Cited by 21 publications

(10 citation statements)

References 2 publications

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“…Furthermore, it has been shown very recently [36] that the Lichtenecker-Rother logarithmic formula [29] can be derived by applying Maxwell's equations and the principle of charge conservation to a mixture in which the shapes and orientations of the components are randomly spatially distributed, and that the symmetric mixture formula of Bruggeman (3) can be obtained from the Lichtenecker-Rother formula. There is also considerable experimental support for the Lichtenecker-Rother formula, based on data for chaotic mixtures with near-spherical inclusions (see references in [33]). According to [34] it is applicable to composites with more than two components.…”

Section: Conductivitymentioning

confidence: 98%

“…Some work on sulgin-talc mixtures [32] suggests that it is indeed applicable to dc conductivity, provided the volume fractions are replaced by weight fractions. It has been criticized on the grounds that there are logical errors in its formulation [25,33]. However, Zakri et al [34] showed that by combining a beta function distribution of the geometrical shapes of inclusions with effective medium theory, and assuming self-consistency, Lichtenecker's formulae [35] can be derived.…”

Section: Conductivitymentioning

confidence: 99%

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Conductivity and space charge in LDPE/BaSrTiO<inf>3</inf> nanocomposites

Fleming

Ammala

Casey

et al. 2010

2010 10th IEEE International Conference on Solid Dielectrics

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Nano-sized BaSrTiO 3 particles and a dispersant were incorporated in samples of low density polyethylene (LDPE). The nanoparticle loading was 2% or 10% by weight, and the dispersant loading was 4 parts per hundred relative to BaSrTiO 3. dc conductivity measurements were made in the temperature range 30-70 o C in vacuum, and in air at 30 o C. The vacuum dc conductivity in LDPE with 0.4% dispersant was approximately five times larger than in LDPE, but in LDPE containing 0.4% dispersant and 10% nanoparticles it was approximately a factor of 6-7 smaller than in LDPE. Since the conductivity of the latter composite was smaller than that of its least conductive component, it may be that the interface regions between the nanoparticles and the LDPE control the dc conductivity. The dispersant and the nanoparticles both increased , the real part of the relative permittivity. The  values for the nanoparticles, implied by the Lichtenecker-Rother equation for a three-part composite, were of order several hundred, much smaller than the value of at least 10,000 quoted by the nanoparticle suppliers. Space charge measurements were made in air using the Laser Intensity Modulation Method (LIMM), and the profiles calculated using the LIMM Monte Carlo method. The maximum space charge density adjacent to the negative poling electrode was 600 C/m 3 , for the pure LDPE and the LDPE with dispersant, and 200 C/m 3 near the positive electrode. The corresponding maxima in samples with dispersant and nanoparticles were approximately an order of magnitude smaller. The Monte Carlo method is more accurate than other methods of analyzing LIMM data, and this may account for the very large densities close to the electrodes.

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Section: Conductivitymentioning

confidence: 98%

Section: Conductivitymentioning

confidence: 99%

Conductivity and space charge in LDPE/BaSrTiO<inf>3</inf> nanocomposites

Fleming

Ammala

Casey

et al. 2010

2010 10th IEEE International Conference on Solid Dielectrics

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“…Criticisms of Lichtenecker-type mixing formulas are available within the scientific literature, one of the most cited being that of Reynolds and Hough (1957) regarding the incorrect assumptions used to derive the theoretical basis of the model. In response, researchers have sought to present corrections to eliminate mathematical inconsistencies (Neelakantaswamy et al, 1985) or theoretical evidence based on the effective medium theory (Zakri et al, 1998), the Maxwell-Garnett equation (Simpkin, 2010), or topology (Goncharenko et al, 2000). Robinson and Friedman (2003) found the Lichtenecker model to show a poor goodness of fit and a lack of a rigorous theoretical basis.…”

Section: Theorymentioning

confidence: 99%

“…However, these models rely on parameters that are difficult to measure or estimate for real soils and therefore are difficult to apply. As pointed out by Neelakantaswamy et al (1985), the Lichtenecker equation has prevailed because it works well for data from soils across a wide range of materials and applications (Wu et al, 2013;Gnusin et al, 2009;Yang et al, 2009;Batsanov et al, 2008;Chao et al, 2008;Zheng et al, 2005;Roth et al, 1990).…”

Section: Theorymentioning

confidence: 99%

Evaluation of Lichtenecker’s Mixing Model for Predicting Effective Permittivitty of Soils at 50 MHz

2015

Trans. ASABE

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Mixing models help describe the contribution of liquid, gas, and solid phases to the bulk dielectric permittivity of porous materials. They are particularly useful when studying the electromagnetic properties of the vadose zone using TDR or GPR techniques. The objective of this research was to evaluate the Lichtenecker Mixing Model applied to undisturbed and repacked soil data collected with a 50 MHz impedance sensor. These data along with four different applications of the Lichtenecker Mixing Model were used to predict the α parameter and/or solid phase permittivity. The four models employed were: (1) the Complex Refractive Index Model, α = 0.5 (CRIM); (2) dual varying of both α and solid phase permittivity (LI); (3) the direct-weighted average model, α = 1 (DW); and (4) a two-phase simplification of the Lichtenecker model (TM). Overall, the CRIM, LI, and TM models estimated the solid phase permittivity, α, and soil bulk permittivity within the ranges previously reported in the scientific literature, while the other model proved to be of little practical value. Further validation with glass beads showed that the simple CRIM model was the best predictor for soil bulk permittivity when compared to the two-parameter LI model. A regression model was also developed that accurately predicted the volumetric water content of glass beads from soil bulk permittivity, solid phase permittivity, and porosity.

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“…Another way to satisfy the upper and lower Weiner bound was also suggested by Bruggeman 20 as a power law relation but was later generalized by Neelakantaswamy, Turkman, and Sarkar (NTS) 21 to…”

Section: ■ Introductionmentioning

confidence: 98%

Modeling Dynamics of Isotropic Dielectrics in a Laminar Heterogeneous Configuration

McKenzie¹,

Zurawsky²,

Mijović³

2012

J. Phys. Chem. B

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The predictive capabilities of models that satisfy the Weiner bounds and Hashin-Shtrikman (HS) bounds were studied for isotropic dielectrics in a laminar heterogeneous configuration oriented perpendicular to the electric field. The dynamics were investigated isothermally using broadband dielectric relaxation spectroscopy (DRS) in the frequency range of 1 MHz to 100 mHz. The molecules chosen for study were low molecular weight glass formers, glycerol, phenyl salicylate, imidazole, and dimethyl sulfoxide, and macromolecules, polymethylhydrosiloxane, polyvinylpyrrolidone-co-vinyl acetate, poly-dl-lactic acid, and poly l-lactic acid. It was found that none of the models were able to adequately predict in entirety the resultant dynamics. Of the models studied, the most successful were the HS upper bound (HSUB), the complementary universal Weiner equation (CWE), and the Lichtenecker model for the dimensional parameter, ζ = -1/2. The least successful models were the upper Weiner bound (UWB), the Neelakantaswamy, Turkman, and Sarkar (NTS) model for ζ = 1/2, and the Lichtenecker model for ζ = 1/2.

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Complex permittivity of a dielectric mixture: corrected version of Lichtenecker's logarithmic law of mixing

Cited by 21 publications

References 2 publications

Conductivity and space charge in LDPE/BaSrTiO<inf>3</inf> nanocomposites

Conductivity and space charge in LDPE/BaSrTiO<inf>3</inf> nanocomposites

Evaluation of Lichtenecker’s Mixing Model for Predicting Effective Permittivitty of Soils at 50 MHz

Modeling Dynamics of Isotropic Dielectrics in a Laminar Heterogeneous Configuration

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