Condition for existence of master curve in conductivity relaxation

The complex conductivity reflects the charge hopping mechanism in the low frequency region. The conditions to appear the relaxation spectrum as H(τ) ∝ τα are discussed based on the mechanisms of phonon-assisted hopping for highly stretchable polyacetylene (hs-PA) and interfibril-barrier hopping for Shirakawa-PA. The hopping (or relaxation) time, r, is a function of hopping distance, r, and hopping energy, E. When the distributions of r and E are independent and the distribution of E is very narrow compared with that of r, isoenergetic hopping appears. If ris represented by a product of τr(r) and τE(E), H (τ) is given by a functionof τ/τE(E0) for isoenergetic hopping, where E0 is a peak energy. The effect of temperature is included only in τ E(E0). Using this result it can be shown that the complex conductivity is reduced to a master curve if the average of xr(r) is independent of temperature, which has been observed in hs-PA film.