Analysis of the ESR linewidth in pristinetrans-polyacetylene

The cw ESR linewidth was studied in detail as a function of frequency and temperature in pristine trans-(CH${)}_{\mathrm{x}}$ and (CD${)}_{\mathrm{x}}$ prepared by the Shirakawa technique. It was demonstrated that all the obtained data could be interpreted by quasi-one-dimensional diffusive motion of the neutral soliton with a diffuse-trap soliton model. An anomalous line broadening below 6 MHz was observed only in trans-(CH${)}_{\mathrm{x}}$. The origin was ascribed to a crossover from “unlike spins” to “like spins” as a relation between electron and nuclear spins. Such an interpretation gives the maximum spin density ${\mathrm{\rho }}_{\max }$≈0.1 of the delocalized neutral soliton. The temperature dependence of the motion-narrowed ESR linewidth ${\mathrm{T}}_2^{\prime \mathrm{-}1}$ was found to be consistent with the phase memory time ${\mathrm{T}}_{\mathrm{M}}^{\mathrm{-}1}$ in terms of the diffuse-trap model. It is discussed that direct evidence of the diffuse-trap model is given by multiple-quantum-spin coherence experiments, although the original authors concluded that all the solitons were trapped both at 4.2 and 300 K. The temperature dependence of the diffusion rage ${\mathrm{D}}_{\mathrm{\parallel }}$ along the polymer chain was found to follow a ${\mathrm{T}}^2$ law. This behavior is consistent with that deduced from the NMR ${\mathrm{T}}_1$ data. With this agreement between the two resonance methods, validity of the applied diffuse-trap model was reconfirmed. Another interpretation for ${\mathrm{D}}_{\mathrm{\parallel }}$ derived from ESR ${\mathrm{T}}_1$ was discussed in connection with the present interpretation. The temperature dependence of the cutoff frequency 1/${\mathrm{\tau }}_{\mathrm{\perp }}$ was interpreted by exchange coupling between the solitons at low temperatures and a phonon-assisted hopping through the charged solitons at high temperatures, as discussed by Kivelson and Heeger.