Abstract: The proton spin-lattice relaxation times in transpolyacetylene versus Larmor frequency ω and temperature T were reported and analyzed by Nechtschein et. al. (2). The ω^-1/2 dependence of the proton spin-lattice relaxation rate T₁^-1 in trans-polyacetylene was obaerved. However, at high frequency the data deviate from ω^-1/2 at a certain frequency which becomes lower and lower as temperature is decreased.
These experimental results are analyzed in a different way in this paper. First, the justification for 1D-soliton diffusion model is discussed. The interpretation whereby only nuclear spin flip diffusion to static paramagnetic centers gives rise to ω^-1/2 behaviour in the proton relaxation rate is ruled out. Solitons can be either in mobile state or in fixed state. As the temperature decreases two effects take place, that is, there are fewer and fewer solitons in the mobile stale and the diffusion coefficient of mobile Solitons decreases. Only diffusive solitons are responsible to the observed proton relaxation, while the contribution from fixed solitos are negligible. Secondly, a 1D random walk model for mobile solitons is described and its correlation function and spectrum density function are calculated. The proton spinlatticc relaxation rate is

where C is the density of mobile soliton, τ is the hopping time of mobile soliton between adjacent sites along the chain, and ω is the Larmor frequency of proton.
Theoretical curves obtained from this formula fit with Nechtscheins measurement very well. The hopping time and relative density of mobile solitons at various temperatures are extracted,