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Journal ArticleDOI

Correlation Function Theory of Dielectric Relaxation

15 Jan 1965-Journal of Chemical Physics (American Institute of Physics)-Vol. 42, Iss: 2, pp 637-643
TL;DR: The Kubo formalism for polarizable dipolar molecules treated as harmonic oscillators in the relaxation counterpart of Kirkwood's equilibrium theory was developed in this article, where the correlation function expression for relaxation was evaluated for several models: rotational transition probabilities including diffusion, nonequivalent dipole orientation sites, and flexible molecules with internal dipole reorientations.
Abstract: The Kubo formalism is developed for polarizable dipolar molecules treated as harmonic oscillators in the relaxation counterpart of Kirkwood's equilibrium theory. Treatment of reaction field induced moments as in Onsager's model gives a generalization of the relaxation time ratio 3e0/(2e0+e∞) proposed by Powles. The correlation function expression for relaxation is evaluated for several models: rotational transition probabilities including diffusion, nonequivalent dipole orientation sites, and flexible molecules with internal dipole reorientations.
Citations
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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: In this paper, a review of the entanglement dynamics of flexible polymer chains from theoretical and experimental points of view is presented, and the validity and limitation of the models are discussed.

590 citations

Journal ArticleDOI
TL;DR: In this article, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present.
Abstract: The frequency dependence of the dielectric response of solids shows an apparently bewildering variety of patterns, virtually none of which corresponds to the classical Debye behaviour. However, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present. This corresponds to power-law dependences on time under step-function excitation and it applies completely generally regardless of the detailed physical and chemical nature of the materials in question and also applies equally to dipoles, ions and hopping electrons as the polarizing species. Moreover, the power-law responses persist down to the lowest temperatures in the milliKelvin range, thus proving the importance of non-thermal transitions. The power laws are characterized by exponents in the range ± 1 and they cover as special cases the complete range of the observed types of response, from virtually frequency-independent “flat” losses often seen in low-loss materials, through various forms of asymmetric loss peaks to strongly dispersive behaviour in which both the real and the imaginary components of the susceptibility vary almost inversely with frequency. The “universality” of the power law strongly suggests the dominance in all materials of a common mechanism of dielectric relaxation and this is found in many-body interactions which provide a model capable of explaining the totality of the observed responses of solids, including both the frequency- and the temperature-dependence. In this interpretation, the classical one-particle Debye law represents but a singularity in a more general behaviour and is usually overshadowed by the new many-body mechanisms.

487 citations

Journal ArticleDOI
TL;DR: The discovery and development of manmade polymer materials dates from the pioneering works of Goodyear (vulcanized rubber) and Hyatt (celluloid plastics) in the mid-nienteenth century, and to Baekeland (Phenol-formaldehyde resins) at the beginning of this century, the remarkable growth of the synthetic fiber, rubber, and plastics industries followed the preparative achievements of the I.C.I.
Abstract: Whilst the discovery and development of manmade polymer materials dates from the pioneering works of Goodyear (vulcanized rubber) and Hyatt (celluloid plastics) in the mid-nienteenth century, and to Baekeland (Phenol-formaldehyde resins) at the beginning of this century, the remarkable growth of the synthetic fiber, rubber and plastics industries followed the preparative achievements of the I.C.I. group in Cheshire (polyethylene), Carothers at Du Pont, Wilmington (linear polyesters and nylons) and the German chemists (polyvinyl halides) in the 1930's, and the U.S. Government Synthetic Rubber Program during World War II. The ability to vary chemical structure and composition (e.g. for copolymers) and physical structure (by fillers, plasticizers, thermal and mechanical treatments, processing methods) made it possible to create materials which could be tailor-made for a particular application. Thus the industries grew to the dominant positions they hold today.

340 citations

Book ChapterDOI
TL;DR: In this article, the constant dielectrique and permittivite des molecules a l'etat liquide are discussed, as well as the permittivity of the molecules.
Abstract: Revue des etudes sur la constante dielectrique et la permittivite des molecules a l'etat liquide. Etudes theoriques

321 citations

References
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Journal ArticleDOI
Ryogo Kubo1
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Abstract: A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.

7,090 citations

Journal ArticleDOI
TL;DR: In this paper, an extension of the Onsager theory of dielectric polarization is presented, which is applied to liquid water under the assumption of tetrahedral coordination and directed bonds between neighboring molecules.
Abstract: An extension of the Onsager theory of dielectric polarization is presented. The local dielectric constant is approximated by the macroscopic dielectric constant of the fluid in a region outside a molecule and its first shell of neighbors rather than in the entire region exterior to the molecule. In addition to the molecular dipole moment, the average value 〈cosγ〉Av of the cosine of the angle between neighbor dipoles is a determining factor. Hindered relative rotation of neighboring molecules produces a correlation between their orientations and prevents 〈cosγ〉Av from vanishing. The theory is applied to liquid water under the assumption of tetrahedral coordination and directed bonds between neighboring molecules.

1,660 citations