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Journal ArticleDOI

Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

01 Apr 1941-Journal of Chemical Physics (American Institute of Physics)-Vol. 9, Iss: 4, pp 341-351
TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...
Citations
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Journal ArticleDOI
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

7,412 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the electrical double-layer at a solid electrode does not in general behave as a pure capacitance but rather as an impedance displaying a frequency-independent phase angle different from 90°.

2,602 citations

Journal ArticleDOI
S. Havriliak1, S. Negami1
01 Jan 1967-Polymer
TL;DR: In this paper, it was shown that the complex deformation of the same data can be represented by a function of same form but with different values for the constants, which can be interpreted as the decay of the distortion with time of the removal of stress field.

2,483 citations

Journal ArticleDOI
TL;DR: The use of bioelectrical impedance analysis (BIA) is widespread both in healthy subjects and patients, but suffers from a lack of standardized method and quality control procedures.

2,371 citations

Book
01 Jan 2011
TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

2,007 citations

References
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Journal ArticleDOI
TL;DR: Extension de la theorie du mouvement brownien de translation and de rotation au cas d'une particule ellipsoidale quelconque Application a l'etude de la dispersion dielectrique pour des molecules polaires ellipssoidales en milieu liquide I - Connaissant les coefficients de frottement de translation (f1, f2, f3 et de rotation (C1, C2, C3) relatifs, le theoreme d'equipartition de 1 energie
Abstract: Extension de la theorie du mouvement brownien de translation et de rotation au cas d'une particule ellipsoidale quelconque Application a l'etude de la dispersion dielectrique pour des molecules polaires ellipsoidales en milieu liquide I - Connaissant les coefficients de frottement de translation (f1, f2, f3 et de rotation (C1, C2, C3) relatifs au mouvement d'un ellipsoide immerge, le theoreme d'equipartition de 1 energie cinetique donne, par la methode de Langevin-Einstein, les valeurs moyennes des carres et produits des composantes de translation et de rotation, suivant ses axes, du deplacement pendant un petit intervalle de temps, d'une particule ellipsoidale en suspension dans un liquide :[FORMULE] Ces valeurs moyennes ne dependent ni de la distribution des masses dans l'interieur de la particule, ni de sa masse totale Les petits deplacements de l'ellipsoide etant determines par rapport a ses axes, dependent de son orientation, mais non de la position de son centre Le mouvement brownien de rotation autour du centre peut donc etre etudie separement, tandis qne celui de translation depend des rotations concomitantes II - En representant les orientations d'un solide par un point sur une hypersphere Σ de l'espace a quatre dimensions, on montre que le mouvement brownien de rotation de l'ellipsoide correspond a un mouvement brownien anisotrope du point representatif Il en resulte pour la densite de probabilite de presence U de ce point, un « courant de diffusion » d, fonction vectorielle lineaire du gradient de U : dρ = Dρσ × [(∂U)/(∂x^σ)]; le tenseur « coefficient de diffusion » Dρσ etant diagonal par rapport aux coordonnees orthogonales locales qui correspondent aux petites rotations de l'ellipsoide autour de ses axes, et ayant comme valeurs principales (∂U)/(∂t) = - div d L'equation de conservation de la densite de probabilite U sur la multiplicite Σ donne une equation aux derivees partielles qui determine la fonction U relative au mouvement brownien de rotation libre de l'ellipsoide En presence d'un champ orientant (molecule polaire dans un champ electrique), il se superpose au courant de diffusion un « courant de convection » c = U v, la vitesse v du point representatif etant determinee, pour chaque position, par l'egalite du couple de frottemnt et du couple orientant L'equation de convervation s'ecrit alors [FORMULE] III - Cette equation reste valable pour un champ variable, tant qu'on peut negliger la duree d'etablissement du mouvement de rotation du au champ Elle permet de determiner en premiere approximation, suivant la methode employee par Debye pour des spheres, la repartition d'un ensemble de molecules ellipsoidales polaires soumises, en milieu liquide, a un champ electrique oscillant de frequence v, et la valeur moyenne correspondante m du moment electrique par molecule dans la direction du champ En designant par m1, m2, m3 les composantes du moment permanent lie a la molecule, suivant ses axes de symetrie on trouve (avec la representation imaginaire des oscillations)[FORMULES] La quantite C jk qui determine le temps de relaxation τi associe a la composante du moment suivant l'axe i, etant la moyenne harmonique des coefficients de frottement de rotation autour des axes j et k perpendiculaires a l'axe i : : 2/(Cjk) = 1/(Cj) + 1/(Ck) La formule qui donne m comprend en general trois termes de dispersion, analogues au terme unique de la formule de Debye valable pour des molecules spheriques Cependant si le moment permanent est dirige suivant un axe de la molecule ellipsoidale il subsiste un seul de ces termes; la dispersion est alors la meme que si les molecules etaient spheriques, seule la valeur du temps de relaxation etant changee Il se trouve meme que pour des molecules ellipsoidales de revolution allongees, ayant un moment perpendiculaire a leur axe de revolution, le temps de relaxation unique dont depend la dispersion a presque la valeur qu'il aurait pour des molecules spheriques de meme volume

1,450 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed a general theory of internal friction in a vibrating body and derived explicit formulae for reeds and wires, and the effect of crystal orientation in single crystal specimens.
Abstract: Stress inhomogeneities in a vibrating body give rise to fluctuations in temperature, and hence to local heat currents. These heat currents increase the entropy of the vibrating solid, and hence are a source of internal friction. The general theory of this internal friction is here developed. The simplest example of stress inhomogeneity is that occurring in the transverse vibrations of reeds and wires. Explicit formulae are obtained for reeds and wires, and the effect is calculated of crystal orientation in single crystal specimens. Microscopic stress inhomogeneities arise from imperfections, such as cavities, and from the elastic anisotropy of the individual crystallites. The internal friction due to spherical cavities is calculated. The internal friction due to elastic anisotropy is investigated for cubic metals, and is found to be greatest for lead, least for aluminum and tungsten.

660 citations

Journal ArticleDOI
01 Aug 1936-Physics
TL;DR: In this article, the transient equation for relaxation processes can be deduced from the experimental impedance formula, and relaxation experiments are in agreement with the deduced transient equation, and the relation of this equation to the well-known Maxwell equation is discussed.
Abstract: An attempt is made to develop a general method of analyzing experimental results concerned with the behavior of elasto‐viscous bodies. It is shown that the transient equation for relaxation processes can be deduced from the experimental impedance formula, and that relaxation experiments are in agreement with the deduced transient equation. A differential equation relating stress, strain and time is derived from the experimental impedance formula. The relation of this equation toithe well‐known Maxwell equation is discussed.

339 citations