Frequency response of hopping systems: Application to polyacetylene

Abstract

Hopping mechanisms for conductivity are characterized by a broad distribution of hopping rates. We have calculated the ratio of the conductivity in the high-frequency regime (frequency greater than the maximum hopping frequency) and its dc value. The results for isoenergetic hopping and variable-range hopping are shown to differ, although both are found to be independent of the details of the hopping attempt frequency. These results are applied to the experimental data for doped trans-polyacetylene. Charge conduction in undoped and lightly doped trans-polyacetylene is in agreement with isoenergetic hopping consistent with intersoliton electron hopping. In contrast, the data for trans-polyacetylene doped to 0.01-0.05 ${\mathrm{I}}_{3}$ per carbon are in better agreement with variable-range hopping, consistent with the proposal of variable-range hopping among pinned solitons. These results support a change in the charge transport mechanism as polyacetylene is doped.