Magnetic-resonance studies in undopedtrans-polyacetylene(CH)x. II

Abstract

Magnetic-resonance data in undoped trans-${\left(\mathrm{CH}\right)}_x$, including nuclear relaxation time ($T_1$) measurements versus frequency and ESR linewidth in the temperature range 300—4.2 K, are reported and analyzed. The results are comprehensively explained in terms of highly-one-dimensional diffusive spins which can be trapped in the presence of impurities, or defects, in particular those connected to oxygen contamination. The average number of diffusive spins, as given by the diffusive-spin population at thermal equilibrium, is a function of temperature through two parameters: the trap-site concentration and the trapping energy. Trap-site concentrations of 5% and 25% have been obtained for samples sealed under vacuum and air-contaminated samples, respectively. The trapping energy is found to be distributed, from chain to chain, from a maximum value $E_0\simeq 0.06$ eV, which likely corresponds to the chain nearest to ${\mathrm{O}}_2$ impurities located at the fibril surface, to about zero for chains far inside the fibril. As the temperature decreases two effects take place, as reflected by the spin-dynamics studies. First, due to the trapping effect, there are fewer and fewer spins in the diffusive state. Second, the diffusion coefficient decreases. Starting from the room-temperature value $\mathcal{D}\sim 5\times {10}^{-3\mathrm{}}$ ${\mathrm{cm}}^2$/s, the decrease is slow at first then for $T<\mathrm{}100\mathrm{}$ K seems to obey a power law $\propto T^2$, similarly to a theoretical result derived by Wada and Schrieffer in the case of Brownian motion of domain walls upon two phonon processes. The spin delocalization has been evaluated for the trapped state from ESR, and for the diffusive state from $T_1$. In both cases the spin density has been found to be delocalized over 10 to 17 CH units. All characteristics and properties determined from the spins in trans-${\left(\mathrm{CH}\right)}_x$ are consistent with the soliton—bond-alternation defect—picture, provided that the trapping effect is taken into account.