Free Volume, Entropy, and Relaxation Phenomena

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Abstract
The Vogel‐Fulcher equation, ln τ∝H/R(T−T 2 ), and the WLF equation, ln τ∝−C 1 (T−T 0 )/[C 2 +(T−T 0 )], can be expressed in the same form. They are known to fit well the relaxation data of liquids in equilibrium. Doolittle's free volume equation, ln τ∝1/f, and Adam‐Gibbs's entropyequation, ln τ∝C/RTS, can be reduced to the Vogel‐Fulcher equation with reasonable assumptions on the temperature dependence of the free volume fraction f and the configurational entropyS. However, in predicting the relaxation behavior in the nonequilibrium state, the Adam‐Gibbs equation predicts an Arrhenius‐type temperature dependence for a fixed structural parameter S, while the Doolittle equation predicts temperature‐independent behavior for a fixed structural parameter f. On the basis of experimental evidence, the Adam‐Gibbs equation is shown to be clearly a better theory than the Doolittle equation. Moreover, with the Adam‐Gibbs equation, it is shown that the kinetic parameters required to describe physical aging are the same as those necessary to describe dielectric relaxation behavior.

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