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Register a new userStretched-exponential decay functions from a self-consistent model of dielectric relaxation
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Added by
Alexander V. Milovanov Dr.
Publication date
2007
fields
Physics
and research's language is
English
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There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives.
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Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A exp [-(t/tau)^{beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corte et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $beta$ that depends on the strain amplitude: $0.25 < beta < 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.
This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a self-consistent dynamical modeling. The key issues are, stretched exponential character of dielectric relaxation, power-law power spectral density, and anomalous dependence of ac conduction coefficient on frequency. We propose a self-consistent model of dielectric relaxation, in which the relaxations are described by a stretched exponential decay function. Mathematically, our study refers to the expanding area of fractional calculus and we propose a systematic derivation of the fractional relaxation and fractional diffusion equations from the property of ac universality.
We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.
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