Dielectric relaxation and dynamic susceptibility of a one-dimensional model for perpendicular-dipole polymers

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Abstract
The dielectric properties of a simple model are studied. The model consists of a one‐dimensional lattice of interacting objects, called spins. Each spin is oriented in a plane perpendicular to the lattice axis and is free to rotate in that plane. The spins undergo harmonic interactions with each other and, if they are dipolar, a cosine interaction with external fields. At sufficiently low temperature and for sufficiently strong spin–spin coupling, the model is equivalent to one in which the spin–spin interactions are proportional to the cosine of the angular difference between spin positions. It is shown that solution of the rotational diffusion equation leads to an interaction‐independent, nonexponential decay function that is quite similar to a decay function derived empirically from polymer data by Williams and his co‐workers. Exact decay functions are derived for both strong and weak applied fields, for both periodic and open boundary conditions, and for both nearest‐neighbor and longer‐range spin–spin interactions. Results of numerical calculations of dynamic susceptibitlity are presented, and it is shown that the model’s qualitative behavior is consistent with much experimental data, especially polymer data.