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Models for Slow Relaxation in Glassy Systems

  • R. G. Palmer
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)

Abstract

Many glassy materials display non-exponential relaxation with a non-Arrhenius temperature dependence. We define a relaxation function q(t) that decays from 1 to 0 to describe (besides initial transients) the scaled response of some quantity y to a step-function change in another quantity x. For example the control variable x might be temperature, strain, or electric field, and the measured quantity y might be volume, strain, or polarization. The relaxation function q(t) may also be extracted from the AC response or from an autocorrelation function 〈y(0)y(t)〉. In simple systems controlled by activation over a single free energy barrier ΔF we expect q(t) = exp(−t/τ) with an Arrhenius temperature dependence τ ∝ exp(ΔF/k B T) for the relaxation time τ. The non-exponential relaxation seen in glassy systems is slower than exponential, in the sense that −q(t)/q′(t) increases with t. In structural glasses, polymers, and dielectrics it is often well described by a stretched exponential, often known as a Kohlrausch [1] law,
$$q(t) = \exp \left[ { - {{(t/\tau )}^\beta }} \right]$$
(1)
, with β < 1. This is slower than exponential but faster than power law or logarithmic (though a stretched exponential with small β is indistinguishable from a logarithmic decay). A value of β from 0.5 to 0.7 is common in glasses, while values around 0.3 are often seen in polymers. The law (1) is the best two-parameter fit known across a wide class of glassy materials and properties. Systematic deviations show that it is not, however, the precise functional form of most data. Particular experimental results may be fitted better by other empirical functions.

Keywords

Random Graph Configuration Space Relaxation Function Cayley Tree Exponential Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • R. G. Palmer
    • 1
  1. 1.Department of PhysicsDuke UniversityDurhamUSA

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