Kinetic Ising model for polymer dynamics. II. Generalized transition rates and the Williams–Watts nonexponential function

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Abstract
We continue our study [J. Chem. Phys. 79, 1955 (1983)] of the one- dimensional kinetic Ising model to investigate cooperative dynamics in amorphous polymers. In this paper we consider the most general single spin-flip model. The spin–spin correlation function is calculated approximately using continued fractions. We find that the Williams–Watts empirical function φ(t)=exp[−(t/τ)β] with 1/2≤β≤1 provides a good fit to this correlation function. The results are interpreted in terms of the dynamics of domain wall defects in which the two fundamental processes are defect migration and defect creation and annihilation. This suggests possible microscopic mechanisms for relaxation in solid amorphous polymers.