ac conductivity of emeraldine polymer

Abstract

An experimental study of the temperature- (T-) dependent dc and audio-frequency conductivity (\ensuremath{\sigma}) as a function of protonation level (0.0\ensuremath{\le}x\ensuremath{\equiv}[${\mathrm{H}}^{+}$]/[N]\ensuremath{\le}0.08) of emeraldine polymer is presented. The dc conductivity varies from ${10}^{\mathrm{\ensuremath{-}}10}$ S/cm for x=0 to ${10}^{\mathrm{\ensuremath{-}}6}$ S/cm for x=0.08 and is proportional to exp[-(${T}_{0}$/T${)}^{1/4}$] with ${T}_{0}$ decreasing with increasing x. The temperature-dependent audiofrequency f (${10}^{1}$--${10}^{5}$ Hz) conductivity varies as ${f}^{s}$ with s\ensuremath{\sim}0.9 for x=0, decreasing with increasing x. For frequencies greater than ${10}^{3}$ Hz the dielectric constant agrees with the T-independent dielectric constant measured by microwave techniques. At lower frequencies and high temperatures the dielectric constant increases. A Cole-Cole analysis shows the presence of primarily a single thermally activated relaxation process in these materials with a dispersion in relaxation rates. These results are discussed in the context of models for dc and ac transport in polymers, with results supporting hopping of charge among positively charged polaron and bipolaron or neutral defect (polaron) states in the emeraldine polymer. A simple analysis yields estimates of 3.7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ bipolarons per polaron in the x=0 system, increasing with protonation to 7.9\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ for x=0.08.